Template:Lognormal distribution estimation of the parameters - Revision history

Lisa Hacker: Redirected page to The Lognormal Distribution

2012-08-03T09:00:59Z

Redirected page to The Lognormal Distribution

← Older revision		Revision as of 09:00, 3 August 2012
Line 1:		Line 1:
	~~==Estimation of the Parameters==~~		#REDIRECT [[The_Lognormal_Distribution]]

	~~{{lognormal distribution probability plotting}}~~

	~~{{lognormal distribution rank regression on Y}}~~

	~~{{lognormal distribution rank regression on x}}~~

	~~{{lognormal distribution maximum likelihood estimation}}~~

Harry Guo at 18:38, 13 February 2012

2012-02-13T18:38:38Z

← Older revision		Revision as of 18:38, 13 February 2012
Line 8:		Line 8:

	{{lognormal distribution maximum likelihood estimation}}		{{lognormal distribution maximum likelihood estimation}}

	~~{{lognormal distribution confidence bounds}}~~

Harry Guo at 17:28, 13 February 2012

2012-02-13T17:28:48Z

← Older revision		Revision as of 17:28, 13 February 2012
Line 1:		Line 1:
	==Estimation of the Parameters==		==Estimation of the Parameters==

	{{ld probability plotting}}		{{lognormal distribution probability plotting}}

	{{ld rank regression on Y}}		{{lognormal distribution rank regression on Y}}

	{{ld rank regression on x}}		{{lognormal distribution rank regression on x}}

	{{ld maximum likelihood estimation}}		{{lognormal distribution maximum likelihood estimation}}

	{{ld confidence bounds}}		{{lognormal distribution confidence bounds}}

Harry Guo: moved Template:Lognormal distributionestimation of the parameters to Template:Lognormal distribution estimation of the parameters

2012-02-10T23:21:58Z

moved Template:Lognormal distributionestimation of the parameters to Template:Lognormal distribution estimation of the parameters

← Older revision	Revision as of 23:21, 10 February 2012
(No difference)

Harry Guo: moved Template:Ld estimation of the parameters to Template:Lognormal distributionestimation of the parameters

2012-02-10T23:18:22Z

moved Template:Ld estimation of the parameters to Template:Lognormal distributionestimation of the parameters

← Older revision	Revision as of 23:18, 10 February 2012
(No difference)

Nicolette Young: /* Confidence Bounds */

2012-01-04T18:35:51Z

Confidence Bounds

Show changes

Nicolette Young: /* Confidence Bounds */

2012-01-04T18:35:05Z

Confidence Bounds

← Older revision		Revision as of 18:35, 4 January 2012
Line 9:		Line 9:
	{{ld maximum likelihood estimation}}		{{ld maximum likelihood estimation}}

	===Confidence Bounds===		==Confidence Bounds==
	The method used by the application in estimating the different types of confidence bounds for lognormally distributed data is presented in this section. Note that there are closed-form solutions for both the normal and lognormal reliability that can be obtained without the use of the Fisher information matrix. However, these closed-form solutions only apply to complete data. To achieve consistent application across all possible data types, Weibull++ always uses the Fisher matrix in computing confidence intervals. The complete derivations were presented in detail for a general function in Chapter 5. For a discussion on exact confidence bounds for the normal and lognormal, see Chapter 8.		The method used by the application in estimating the different types of confidence bounds for lognormally distributed data is presented in this section. Note that there are closed-form solutions for both the normal and lognormal reliability that can be obtained without the use of the Fisher information matrix. However, these closed-form solutions only apply to complete data. To achieve consistent application across all possible data types, Weibull++ always uses the Fisher matrix in computing confidence intervals. The complete derivations were presented in detail for a general function in Chapter 5. For a discussion on exact confidence bounds for the normal and lognormal, see Chapter 8.

Nicolette Young at 18:34, 4 January 2012

2012-01-04T18:34:03Z

← Older revision		Revision as of 18:34, 4 January 2012
Line 7:		Line 7:
	{{ld rank regression on x}}		{{ld rank regression on x}}

	~~===Maximum Likelihood Estimation===~~		{{ld maximum likelihood estimation}}
	~~As it was outlined in Chapter 3,~~ maximum likelihood estimation works by developing a likelihood function based on the available data and finding the values of the parameter estimates that maximize the likelihood function. This can be achieved by using iterative methods to determine the parameter estimate values that maximize the likelihood function. However, this can be rather difficult and time-consuming, particularly when dealing with the three-parameter distribution. Another method of finding the parameter estimates involves taking the partial derivatives of the likelihood equation with respect to the parameters, setting the resulting equations equal to zero, and solving simultaneously to determine the values of the parameter estimates. The log-likelihood functions and associated partial derivatives used to determine maximum likelihood estimates for the lognormal distribution are covered in Appendix C.

	===Confidence Bounds===		===Confidence Bounds===

Nicolette Young at 18:32, 4 January 2012

2012-01-04T18:32:38Z

@@ Line 5: / Line 5: @@
 {{ld rank regression on Y}}
+{{ld rank regression on x}}
 ===Maximum Likelihood Estimation===

Nicolette Young at 18:31, 4 January 2012

2012-01-04T18:31:43Z

Show changes