Electronic settlement of petroleum and gas distributions

• US 7,676,420 B1
• Filed: 06/19/2003
• Issued: 03/09/2010
• Est. Priority Date: 06/19/2002
• Status: Active Grant

• Current Assignee: Accenture Global Services Limited (Accenture PLC)
• Original Assignee: Accenture Global Services GmbH (Accenture PLC)
• Inventors: Agnew, Thomas J., Agnew, Frank D.
• Primary Examiner(s): Kyle; Charles R
• Assistant Examiner(s): PERRY, LINDA C
• Application Number:
  US10/465,296
• Time in Patent Office: 2,455 Days
• Field of Search: None
• US Class Current: 705/37
• CPC Class Codes: G06Q 40/00 Finance; Insurance; Tax strategies; Processing of corporate or income taxes
• CPC Class Codes: G06Q 40/04 Trading; Exchange, e.g. stocks, commodities, derivatives or currency exchange

Abstract

In one embodiment, a system can include a centralized storage module, for example a database, that stores data relating to petroleum, natural gas and other related products taken from several different sources and entities. The entity storing and maintaining this data can be an entity independent from the operators, producers and/or other working interests. This system can use automated techniques to reconcile distributions to all entities associated with a well due to the removal of a mineral, for example, petroleum, natural gas and/or other related products, from that well, on a periodic basis. These automated techniques include, for example, reconciling all agreements associated with the well, reconciling the amount of mineral removed at the well, reconciling the spot market price associated with the well at the time of removal, automating approval by the removing entity, automating payment and the like.

Claims

1. A method for automatically reconciling volume data to ascertain a quantity of mineral associated with a well, the method comprising:

receiving, from a provider of a mineral in a mineral sale, a first volume measurement of the mineral exchanged in the mineral sale;

receiving, from a recipient of the mineral in the mineral sale, a second volume measurement of the mineral exchanged in the mineral sale, the second volume measurement being different than the first volume measurement;

accessing, using an electronic settlement system, an automatic resolution rule defined to reconcile differences in volume measurements received from the provider and volume measurements received from the recipient in the mineral sale;

based on the automatic resolution rule, automatically determining, using the electronic settlement system, a third volume measurement of the mineral exchanged in the mineral sale, the third volume measurement being different than at least one of the first and second volume measurements;

determining, using the electronic settlement system, an estimated market value for minerals extracted from a well from which the mineral exchanged in the mineral sale was extracted;

computing, using the electronic settlement system, a settlement value for the mineral sale using the third volume measurement as a volume of mineral exchanged in the mineral sale and using the estimated market value as a price of the mineral exchanged in the mineral sale; and

electronically settling, using the electronic settlement system, the mineral sale between the provider and the recipient by enabling electronic transfer of funds from the recipient to the provider based on the computed settlement value,

wherein determining an estimated market value for minerals extracted from the well from which the mineral exchanged in the mineral sale was extracted comprises;

identifying market centers serving the well from which the mineral exchanged in the mineral sale was extracted;

receiving local cost data related to extracting minerals from the well and transporting minerals from the well to the identified market centers serving the well;

receiving global price data including price data from each of the identified market centers serving the well;

determining a general pattern of product flow of minerals extracted from the well to each of the identified market centers serving the well, the general pattern of product flow indicating which percentage of minerals extracted from the well travel to which of the identified market centers serving the well; and

determining an estimated market value by performing a statistical interpolation of the local cost data and the global price data that accounts for the determined general pattern of product flow, variability of the local cost data and the global price data, and errors associated with the local cost data and the global price data.

2. The method of claim 1 wherein automatically determining a third volume measurement of the mineral exchanged in the mineral sale further comprises using a liquid, gas and solid balancing technique.

3. The method of claim 1 wherein:

accessing an automatic resolution rule comprises accessing an automatic resolution rule indicating that differences in volume measurements received from the provider and volume measurements received from the recipient are reconciled by taking a weighted average of conflicting volume measurements; and

based on the automatic resolution rule, automatically determining a third volume measurement of the mineral exchanged in the mineral sale comprises computing a weighted average using the first and second volume measurements and first and second weights.

4. The method of claim 1 further comprising:

automatically adjusting the first volume measurement using a first conversion rule that defines an adjustment needed to conform the first volume measurement to a basis;

automatically adjusting the second volume measurement using a second conversion rule that defines an adjustment needed to conform the second volume measurement to the basis,

wherein automatically determining a third volume measurement of the mineral exchanged in the mineral sale comprises automatically determining a third volume measurement based on the adjusted first volume measurement and the adjusted second volume measurement.

5. The method of claim 4 wherein:

automatically adjusting the first volume measurement using a first conversion rule that defines an adjustment needed to conform the first volume measurement to a basis comprises converting the first volume measurement to a unit of measurement; and

automatically adjusting the second volume measurement using a second conversion rule that defines an adjustment needed to conform the second volume measurement to the basis comprises converting the second volume measurement to the unit of measurement.

6. The method of claim 4 wherein:

automatically adjusting the first volume measurement using a first conversion rule that defines an adjustment needed to conform the first volume measurement to a basis comprises correcting the first volume measurement to account for operating conditions at which the first volume measurement was taken; and

automatically adjusting the second volume measurement using a second conversion rule that defines an adjustment needed to conform the second volume measurement to the basis comprises correcting the second volume measurement to account for operating conditions at which the second volume measurement was taken.

7. The method of claim 6 wherein:

correcting the first volume measurement to account for operating conditions at which the first volume measurement was taken comprises correcting the first volume measurement to account for a temperature at which the first volume measurement was taken; and

correcting the second volume measurement to account for operating conditions at which the second volume measurement was taken comprises correcting the second volume measurement to account for a temperature at which the second volume measurement was taken.

8. The method of claim 6 wherein:

correcting the first volume measurement to account for operating conditions at which the first volume measurement was taken comprises correcting the first volume measurement to account for a pressure at which the first volume measurement was taken; and

correcting the second volume measurement to account for operating conditions at which the second volume measurement was taken comprises correcting the second volume measurement to account for a pressure at which the second volume measurement was taken.

9. The method of claim 1 wherein accessing an automatic resolution rule defined to reconcile differences in volume measurements received from the provider and volume measurements received from the recipient in the mineral sale comprises accessing an automatic resolution rule defined based on an agreement between the provider and the recipient.

10. The method of claim 1 wherein accessing an automatic resolution rule defined to reconcile differences in volume measurements received from measurements data received from the recipient in the mineral sale comprises accessing an automatic resolution rule defined based on legal rules that govern the mineral sale.

11. The method of claim 1 wherein automatically determining a third volume measurement of the mineral exchanged in the mineral sale further comprises using a mass and heating balancing technique.

12. The method of claim 1 wherein accessing an automatic resolution rule, automatically determining a third volume measurement, determining an estimated market value, computing a settlement value, and electronically settling the mineral sale occur without human intervention.

13. The method of claim 1 wherein accessing an automatic resolution rule, automatically determining a third volume measurement, determining an estimated market value, computing a settlement value, and electronically settling the mineral sale occur without further input from the provider and the recipient.

14. The method of claim 1 wherein electronically settling the mineral sale between the provider and the recipient comprises electronically transferring the computed settlement value from an account associated with the recipient to an account associated with the provider.

15. The method of claim 14 wherein electronically transferring the computed settlement value from an account associated with the recipient to an account associated with the provider occurs without human intervention.

16. The method of claim 14 wherein electronically transferring the computed settlement value from an account associated with the recipient to an account associated with the provider occurs without further input from the provider and the recipient.

17. The method of claim 1 wherein determining an estimated market value for the mineral exchanged in the mineral sale comprises accounting for taxes, royalties, and settlement values for a variety of lease and agreement provisions.

18. The method of claim 1 wherein determining an estimated market value for the mineral exchanged in the mineral sale comprises determining an estimated market value for the mineral exchanged in the mineral sale based on a highest price in an area of the mineral sale, a most favored nations clause, a major portions pricing, a best commercially available price, and a fair market value at a well operated by the provider.

19. The method of claim 1 wherein determining an estimated market value for the mineral exchanged in the mineral sale comprises determining an estimated market value using market price data received from a source that is independent of the provider and the recipient.

20. The method of claim 1 wherein automatically determining a third volume measurement of the mineral exchanged in the mineral sale comprises automatically determining a third volume measurement of the mineral exchanged in the mineral sale, the third volume measurement being different than both the first and second volume measurements.

21. The method of claim 1 wherein receiving global price data including price data from each of the identified market centers serving the well comprises selecting monitoring points providing the global price data, wherein each monitoring point provides a respective price per volume of mineral and at least one monitoring point corresponds to an independent entity that has no relationship to ownership interests or parties having rights and responsibilities associated with the well from which the mineral exchanged in the mineral sale was extracted.

22. The method of claim 21 wherein selecting monitoring points comprises selecting monitoring points such that no single entity controls the global price data.

23. The method of claim 1 wherein determining an estimated market value by performing a statistical interpolation of the local cost data and the global price data that accounts for the determined general pattern of product flow, variability of the local cost data and the global price data, and errors associated with the local cost data and the global price data comprises determining an estimated market value per unit volume of production.

24. The method of claim 1 wherein determining an estimated market value by performing a statistical interpolation of the local cost data and the global price data that accounts for the determined general pattern of product flow, variability of the local cost data and the global price data, and errors associated with the local cost data and the global price data comprises performing a statistical interpolation that accounts for variability of the local cost data and the global price data that is characterized by minimum, maximum, average, and standard deviation statistics.

25. The method of claim 1 wherein determining an estimated market value by performing a statistical interpolation of the local cost data and the global price data that accounts for the determined general pattern of product flow, variability of the local cost data and the global price data, and errors associated with the local cost data and the global price data comprises performing a statistical interpolation using an estimated probability density function.

26. A computer readable storage medium encoded with a computer program product, the computer program product comprising instructions that, when executed, operate to cause a computer to perform operations comprising:

receiving, from a provider of a mineral in a mineral sale, a first volume measurement of the mineral exchanged in the mineral sale;

receiving, from a recipient of the mineral in the mineral sale, a second volume measurement of the mineral exchanged in the mineral sale, the second volume measurement being different than the first volume measurement;

accessing an automatic resolution rule defined to reconcile differences in volume measurements received from the provider and volume measurements received from the recipient in the mineral sale;

based on the automatic resolution rule, automatically determining a third volume measurement of the mineral exchanged in the mineral sale, the third volume measurement being different than at least one of the first and second volume measurements;

determining an estimated market value for minerals extracted from a well from which the mineral exchanged in the mineral sale was extracted;

computing a settlement value for the mineral sale using the third volume measurement as a volume of mineral exchanged in the mineral sale and using the estimated market value as a price of the mineral exchanged in the mineral sale; and

electronically settling the mineral sale between the provider and the recipient by enabling electronic transfer of funds from the recipient to the provider based on the computed settlement value,

wherein determining an estimated market value for minerals extracted from the well from which the mineral exchanged in the mineral sale was extracted comprises;

identifying market centers serving the well from which the mineral exchanged in the mineral sale was extracted;

receiving local cost data related to extracting minerals from the well and transporting minerals from the well to the identified market centers serving the well;

receiving global price data including price data from each of the identified market centers serving the well;

determining a general pattern of product flow of minerals extracted from the well to each of the identified market centers serving the well, the general pattern of product flow indicating which percentage of minerals extracted from the well travel to which of the identified market centers serving the well; and

determining an estimated market value by performing a statistical interpolation of the local cost data and the global price data that accounts for the determined general pattern of product flow, variability of the local cost data and the global price data, and errors associated with the local cost data and the global price data.

27. The computer readable storage medium of claim 26 wherein automatically determining a third volume measurement of the mineral exchanged in the mineral sale further comprises using a liquid, gas and solid balancing technique.

28. The computer readable storage medium of claim 26 wherein:

accessing an automatic resolution rule comprises accessing an automatic resolution rule indicating that differences in volume measurements received from the provider and volume measurements received from the recipient are reconciled by taking a weighted average of conflicting volume measurements; and

based on the automatic resolution rule, automatically determining a third volume measurement of the mineral exchanged in the mineral sale comprises computing a weighted average using the first and second volume measurements and first and second weights.

29. The computer readable storage medium of claim 26 wherein the operations further comprise:

automatically adjusting the first volume measurement using a first conversion rule that defines an adjustment needed to conform the first volume measurement to a basis;

automatically adjusting the second volume measurement using a second conversion rule that defines an adjustment needed to conform the second volume measurement to the basis,

wherein automatically determining a third volume measurement of the mineral exchanged in the mineral sale comprises automatically determining a third volume measurement based on the adjusted first volume measurement and the adjusted second volume measurement.

30. The computer readable storage medium of claim 29 wherein:

automatically adjusting the first volume measurement using a first conversion rule that defines an adjustment needed to conform the first volume measurement to a basis comprises converting the first volume measurement to a unit of measurement; and

automatically adjusting the second volume measurement using a second conversion rule that defines an adjustment needed to conform the second volume measurement to the basis comprises converting the second volume measurement to the unit of measurement.

31. The computer readable storage medium of claim 29 wherein:

automatically adjusting the first volume measurement using a first conversion rule that defines an adjustment needed to conform the first volume measurement to a basis comprises correcting the first volume measurement to account for operating conditions at which the first volume measurement was taken; and

automatically adjusting the second volume measurement using a second conversion rule that defines an adjustment needed to conform the second volume measurement to the basis comprises correcting the second volume measurement to account for operating conditions at which the second volume measurement was taken.

32. The computer readable storage medium of claim 31 wherein:

correcting the first volume measurement to account for operating conditions at which the first volume measurement was taken comprises correcting the first volume measurement to account for a temperature at which the first volume measurement was taken; and

correcting the second volume measurement to account for operating conditions at which the second volume measurement was taken comprises correcting the second volume measurement to account for a temperature at which the second volume measurement was taken.

33. The computer readable storage medium of claim 31 wherein:

correcting the first volume measurement to account for operating conditions at which the first volume measurement was taken comprises correcting the first volume measurement to account for a pressure at which the first volume measurement was taken; and

correcting the second volume measurement to account for operating conditions at which the second volume measurement was taken comprises correcting the second volume measurement to account for a pressure at which the second volume measurement was taken.

34. The computer readable storage medium of claim 26 wherein accessing an automatic resolution rule defined to reconcile differences in volume measurements received from the provider and volume measurements received from the recipient in the mineral sale comprises accessing an automatic resolution rule defined based on an agreement between the provider and the recipient.

35. The computer readable storage medium of claim 26 wherein accessing an automatic resolution rule defined to reconcile differences in volume measurements received from measurements data received from the recipient in the mineral sale comprises accessing an automatic resolution rule defined based on legal rules that govern the mineral sale.

36. The computer readable storage medium of claim 26 wherein automatically determining a third volume measurement of the mineral exchanged in the mineral sale further comprises using a mass and heating balancing technique.

37. The computer readable storage medium of claim 26 wherein electronically settling the mineral sale between the provider and the recipient comprises electronically transferring the computed settlement value from an account associated with the recipient to an account associated with the provider.

38. The computer readable storage medium of claim 26 wherein determining an estimated market value for the mineral exchanged in the mineral sale comprises accounting for taxes, royalties, and settlement values for a variety of lease and agreement provisions.

39. The computer readable storage medium of claim 26 wherein determining an estimated market value for the mineral exchanged in the mineral sale comprises determining an estimated market value for the mineral exchanged in the mineral sale based on a highest price in an area of the mineral sale, a most favored nations clause, a major portions pricing, a best commercially available price, and a fair market value at a well operated by the provider.

40. The computer readable storage medium of claim 26 wherein determining an estimated market value for the mineral exchanged in the mineral sale comprises determining an estimated market value using market price data received from a source that is independent of the provider and the recipient.

41. The computer readable storage medium of claim 26 wherein automatically determining a third volume measurement of the mineral exchanged in the mineral sale comprises automatically determining a third volume measurement of the mineral exchanged in the mineral sale, the third volume measurement being different than both the first and second volume measurements.

42. The computer readable storage medium of claim 26 wherein receiving global price data including price data from each of the identified market centers serving the well comprises selecting monitoring points providing the global price data, wherein each monitoring point provides a respective price per volume of mineral and at least one monitoring point corresponds to an independent entity that has no relationship to ownership interests or parties having rights and responsibilities associated with the well from which the mineral exchanged in the mineral sale was extracted.

43. The computer readable storage medium of claim 42 wherein selecting monitoring points comprises selecting monitoring points such that no single entity controls the global price data.

44. The computer readable storage medium of claim 26 wherein determining an estimated market value by performing a statistical interpolation of the local cost data and the global price data that accounts for the determined general pattern of product flow, variability of the local cost data and the global price data, and errors associated with the local cost data and the global price data comprises determining an estimated market value per unit volume of production.

45. The computer readable storage medium of claim 26 wherein determining an estimated market value by performing a statistical interpolation of the local cost data and the global price data that accounts for the determined general pattern of product flow, variability of the local cost data and the global price data, and errors associated with the local cost data and the global price data comprises performing a statistical interpolation that accounts for variability of the local cost data and the global price data that is characterized by minimum, maximum, average, and standard deviation statistics.

46. The computer readable storage medium of claim 26 wherein determining an estimated market value by performing a statistical interpolation of the local cost data and the global price data that accounts for the determined general pattern of product flow, variability of the local cost data and the global price data, and errors associated with the local cost data and the global price data comprises performing a statistical interpolation using an estimated probability density function.

47. An electronic settlement system comprising:

at least one computer readable storage medium encoded with executable instructions; and

at least one processor that is configured to, upon execution of the executable instructions, perform operations comprising;

receiving, from a provider of a mineral in a mineral sale, a first volume measurement of the mineral exchanged in the mineral sale;

receiving, from a recipient of the mineral in the mineral sale, a second volume measurement of the mineral exchanged in the mineral sale, the second volume measurement being different than the first volume measurement;

accessing an automatic resolution rule defined to reconcile differences in volume measurements received from the provider and volume measurements received from the recipient in the mineral sale;

based on the automatic resolution rule, automatically determining a third volume measurement of the mineral exchanged in the mineral sale, the third volume measurement being different than at least one of the first and second volume measurements;

determining an estimated market value for minerals extracted from a well from which the mineral exchanged in the mineral sale was extracted;

computing a settlement value for the mineral sale using the third volume measurement as a volume of mineral exchanged in the mineral sale and using the estimated market value as a price of the mineral exchanged in the mineral sale; and

electronically settling the mineral sale between the provider and the recipient by enabling electronic transfer of funds from the recipient to the provider based on the computed settlement value,

wherein determining an estimated market value for minerals extracted from the well from which the mineral exchanged in the mineral sale was extracted comprises;

identifying market centers serving the well from which the mineral exchanged in the mineral sale was extracted;

receiving local cost data related to extracting minerals from the well and transporting minerals from the well to the identified market centers serving the well;

receiving global price data including price data from each of the identified market centers serving the well;

determining a general pattern of product flow of minerals extracted from the well to each of the identified market centers serving the well, the general pattern of product flow indicating which percentage of minerals extracted from the well travel to which of the identified market centers serving the well; and

determining an estimated market value by performing a statistical interpolation of the local cost data and the global price data that accounts for the determined general pattern of product flow, variability of the local cost data and the global price data, and errors associated with the local cost data and the global price data.

48. The device of claim 47 wherein the processor is configured to automatically determine a third volume measurement of the mineral exchanged in the mineral sale using a liquid, gas and solid balancing technique.

49. The device of claim 47 wherein the processor is configured to:

access an automatic resolution rule by accessing an automatic resolution rule indicating that differences in volume measurements received from the provider and volume measurements received from the recipient are reconciled by taking a weighted average of conflicting volume measurements; and

automatically determine a third volume measurement of the mineral exchanged in the mineral sale by computing a weighted average using the first and second volume measurements and first and second weights.

50. The device of claim 47 wherein the processor is configured to:

automatically adjust the first volume measurement using a first conversion rule that defines an adjustment needed to conform the first volume measurement to a basis;

automatically adjust the second volume measurement using a second conversion rule that defines an adjustment needed to conform the second volume measurement to the basis,

wherein the processor is configured to automatically determine a third volume measurement of the mineral exchanged in the mineral sale by automatically determining a third volume measurement based on the adjusted first volume measurement and the adjusted second volume measurement.

51. The device of claim 50 wherein the processor is configured to:

automatically adjust the first volume measurement using a first conversion rule that defines an adjustment needed to conform the first volume measurement to a basis by converting the first volume measurement to a unit of measurement; and

automatically adjust the second volume measurement using a second conversion rule that defines an adjustment needed to conform the second volume measurement to the basis by converting the second volume measurement to the unit of measurement.

52. The device of claim 50 wherein the processor is configured to:

automatically adjust the first volume measurement using a first conversion rule that defines an adjustment needed to conform the first volume measurement to a basis by correcting the first volume measurement to account for operating conditions at which the first volume measurement was taken; and

automatically adjust the second volume measurement using a second conversion rule that defines an adjustment needed to conform the second volume measurement to the basis by correcting the second volume measurement to account for operating conditions at which the second volume measurement was taken.

53. The device of claim 52 wherein the processor is configured to:

correct the first volume measurement to account for operating conditions at which the first volume measurement was taken by correcting the first volume measurement to account for a temperature at which the first volume measurement was taken; and

correct the second volume measurement to account for operating conditions at which the second volume measurement was taken by correcting the second volume measurement to account for a temperature at which the second volume measurement was taken.

54. The device of claim 52 wherein the processor is configured to:

correct the first volume measurement to account for operating conditions at which the first volume measurement was taken by correcting the first volume measurement to account for a pressure at which the first volume measurement was taken; and

correct the second volume measurement to account for operating conditions at which the second volume measurement was taken by correcting the second volume measurement to account for a pressure at which the second volume measurement was taken.

55. The device of claim 47 wherein the processor is configured to access an automatic resolution rule defined to reconcile differences in volume measurements received from the provider and volume measurements received from the recipient in the mineral sale by accessing an automatic resolution rule defined based on an agreement between the provider and the recipient.

56. The device of claim 47 wherein the processor is configured to access an automatic resolution rule defined to reconcile differences in volume measurements received from measurements data received from the recipient in the mineral sale by accessing an automatic resolution rule defined based on legal rules that govern the mineral sale.

57. The device of claim 47 wherein the processor is configured to automatically determine a third volume measurement of the mineral exchanged in the mineral sale using a mass and heating balancing technique.

58. The device of claim 47 wherein the processor is configured to electronically settle the mineral sale between the provider and the recipient by electronically transferring the computed settlement value from an account associated with the recipient to an account associated with the provider.

59. The device of claim 47 wherein the processor is configured to determine an estimated market value for the mineral exchanged in the mineral sale by accounting for taxes, royalties, and settlement values for a variety of lease and agreement provisions.

60. The device of claim 47 wherein the processor is configured to determine an estimated market value for the mineral exchanged in the mineral sale by determining an estimated market value for the mineral exchanged in the mineral sale based on a highest price in an area of the mineral sale, a most favored nations clause, a major portions pricing, a best commercially available price, and a fair market value at a well operated by the provider.

61. The device of claim 47 wherein the processor is configured to determine an estimated market value for the mineral exchanged in the mineral sale by determining an estimated market value using market price data received from a source that is independent of the provider and the recipient.

62. The device of claim 47 wherein the processor is configured to automatically determine a third volume measurement of the mineral exchanged in the mineral sale by automatically determining a third volume measurement of the mineral exchanged in the mineral sale, the third volume measurement being different than both the first and second volume measurements.

63. The device of claim 47 wherein the processor is configured to receive global price data including price data from each of the identified market centers serving the well by selecting monitoring points providing the global price data, wherein each monitoring point provides a respective price per volume of mineral and at least one monitoring point corresponds to an independent entity that has no relationship to ownership interests or parties having rights and responsibilities associated with the well from which the mineral exchanged in the mineral sale was extracted.

64. The device of claim 63 wherein the processor is configured to select monitoring points by selecting monitoring points such that no single entity controls the global price data.

65. The device of claim 47 wherein the processor is configured to determine an estimated market value by performing a statistical interpolation of the local cost data and the global price data that accounts for the determined general pattern of product flow, variability of the local cost data and the global price data, and errors associated with the local cost data and the global price data by determining an estimated market value per unit volume of production.

66. The device of claim 47 wherein the processor is configured to determine an estimated market value by performing a statistical interpolation of the local cost data and the global price data that accounts for the determined general pattern of product flow, variability of the local cost data and the global price data, and errors associated with the local cost data and the global price data by performing a statistical interpolation that accounts for variability of the local cost data and the global price data that is characterized by minimum, maximum, average, and standard deviation statistics.

67. The device of claim 47 wherein the processor is configured to determine an estimated market value by performing a statistical interpolation of the local cost data and the global price data that accounts for the determined general pattern of product flow, variability of the local cost data and the global price data, and errors associated with the local cost data and the global price data by performing a statistical interpolation using an estimated probability density function.