Template:Lognormal distribution characteristics - Revision history

Richard House: Redirected page to Lognormal Distribution Characteristics

2012-08-13T05:33:52Z

Redirected page to Lognormal Distribution Characteristics

← Older revision		Revision as of 05:33, 13 August 2012
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	~~==Characteristics of~~ Lognormal Distribution ==		#REDIRECT [[Lognormal Distribution Characteristics]]
	~~[[Image:WB.10 effect of sigma.png\|center\|250px\| ]]~~
	~~<math></math>~~

	~~:• The lognormal distribution is a distribution skewed to the right.~~
	~~:• The <math>pdf</math> starts at zero, increases to its mode, and decreases thereafter.~~
	~~:• The degree of skewness increases as <math>{{\sigma'}}</math> increases, for a given <math>\mu'</math>~~

	~~[[Image:WB.10 lognormal pdf.png\|center\|250px\|~~ ]]

	~~:• For the same <math>{{\sigma'}}</math> , the <math>pdf</math> 's skewness increases as <math>{\mu }'</math> increases.~~
	:• For <math>{{\sigma' }}</math> values significantly greater than 1, the <math>pdf</math> rises very sharply in the beginning, i.e. for very small values of <math>T</math> near zero, and essentially follows the ordinate axis, peaks out early, and then decreases sharply like an exponential <math>pdf</math> or a Weibull <math>pdf</math> with <math>0<\beta <1</math> .
	:• The parameter, <math>{\mu }'</math>, in terms of the logarithm of the <math>{T}'s</math> is also the scale parameter, and not the location parameter as in the case of the normal <math>pdf</math> .
	:• The parameter <math>{{\sigma'}}</math>, or the standard deviation of the <math>{T}'s</math> in terms of their logarithm or of their <math>{T}'</math>, is also the shape parameter and not the scale parameter, as in the normal <math>pdf</math>, and assumes only positive values.


	~~'''Lognormal Distribution Parameters in Weibull++'''~~

	In Weibull++, the parameters returned for the lognormal distribution are always logarithmic. That is: the parameter <math>{\mu }'</math> represents the mean of the natural logarithms of the times-to-failure, while <math>{{\sigma' }}</math> represents the standard deviation of these data point logarithms. Specifically, the returned <math>{{\sigma' }}</math> is the square root of the variance of the natural logarithms of the data points. Even though the application denotes these values as mean and standard deviation, the user is reminded that these are given as the parameters of the distribution, and are thus the mean and standard deviation of the natural logarithms of the data. The mean value of the times-to-failure, not used as a parameter, as well as the standard deviation can be obtained through the QCP or the Function Wizard.

Nicolette Young: /* Characteristics of Lognormal Distribution */

2012-04-25T21:16:47Z

Characteristics of Lognormal Distribution

← Older revision		Revision as of 21:16, 25 April 2012
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	==Characteristics of Lognormal Distribution ==		==Characteristics of Lognormal Distribution ==
	[[Image:WB.10 effect of sigma.png\|center\|~~400px~~\| ]]		[[Image:WB.10 effect of sigma.png\|center\|250px\| ]]
	<math></math>		<math></math>

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	:• The degree of skewness increases as <math>{{\sigma'}}</math> increases, for a given <math>\mu'</math>		:• The degree of skewness increases as <math>{{\sigma'}}</math> increases, for a given <math>\mu'</math>

	[[Image:WB.10 lognormal pdf.png\|center\|~~400px~~\| ]]		[[Image:WB.10 lognormal pdf.png\|center\|250px\| ]]

	:• For the same <math>{{\sigma'}}</math> , the <math>pdf</math> 's skewness increases as <math>{\mu }'</math> increases.		:• For the same <math>{{\sigma'}}</math> , the <math>pdf</math> 's skewness increases as <math>{\mu }'</math> increases.

Nikki Helms: /* Characteristics of Lognormal Distribution */

2012-03-30T21:26:55Z

Characteristics of Lognormal Distribution

← Older revision		Revision as of 21:26, 30 March 2012
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	==Characteristics of Lognormal Distribution ==		==Characteristics of Lognormal Distribution ==
	[[Image:WB.10 effect of sigma.png\|400px\| ]]		[[Image:WB.10 effect of sigma.png\|center\|400px\| ]]
	<math></math>		<math></math>

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	:• The degree of skewness increases as <math>{{\sigma'}}</math> increases, for a given <math>\mu'</math>		:• The degree of skewness increases as <math>{{\sigma'}}</math> increases, for a given <math>\mu'</math>

	[[Image:WB.10 lognormal pdf.png\|400px\| ]]		[[Image:WB.10 lognormal pdf.png\|center\|400px\| ]]

	:• For the same <math>{{\sigma'}}</math> , the <math>pdf</math> 's skewness increases as <math>{\mu }'</math> increases.		:• For the same <math>{{\sigma'}}</math> , the <math>pdf</math> 's skewness increases as <math>{\mu }'</math> increases.

Nicolette Young: /* Characteristics of Lognormal Distribution */

2012-03-14T19:07:16Z

Characteristics of Lognormal Distribution

← Older revision		Revision as of 19:07, 14 March 2012
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	==Characteristics of Lognormal Distribution ==		==Characteristics of Lognormal Distribution ==
	[[Image:WB.10 effect of sigma.png\|~~center\|300px~~\| ]]		[[Image:WB.10 effect of sigma.png\|400px\| ]]
	<math></math>		<math></math>

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	:• The degree of skewness increases as <math>{{\sigma'}}</math> increases, for a given <math>\mu'</math>		:• The degree of skewness increases as <math>{{\sigma'}}</math> increases, for a given <math>\mu'</math>

	[[Image:WB.10 lognormal pdf.png\|~~center\|300px~~\| ]]		[[Image:WB.10 lognormal pdf.png\|400px\| ]]

	:• For the same <math>{{\sigma'}}</math> , the <math>pdf</math> 's skewness increases as <math>{\mu }'</math> increases.		:• For the same <math>{{\sigma'}}</math> , the <math>pdf</math> 's skewness increases as <math>{\mu }'</math> increases.

Nicolette Young: /* Characteristics of Lognormal Distribution */

2012-03-14T19:06:19Z

Characteristics of Lognormal Distribution

← Older revision		Revision as of 19:06, 14 March 2012
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	==Characteristics of Lognormal Distribution ==		==Characteristics of Lognormal Distribution ==
	[[Image:~~ldaDC~~.~~gif\|thumb~~\|center\|300px\| ]]		[[Image:WB.10 effect of sigma.png\|center\|300px\| ]]
	<math></math>		<math></math>

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	:• The degree of skewness increases as <math>{{\sigma'}}</math> increases, for a given <math>\mu'</math>		:• The degree of skewness increases as <math>{{\sigma'}}</math> increases, for a given <math>\mu'</math>

	[[Image:~~ldaDC2~~.~~gif\|thumb~~\|center\|300px\| ]]		[[Image:WB.10 lognormal pdf.png\|center\|300px\| ]]

	:• For the same <math>{{\sigma'}}</math> , the <math>pdf</math> 's skewness increases as <math>{\mu }'</math> increases.		:• For the same <math>{{\sigma'}}</math> , the <math>pdf</math> 's skewness increases as <math>{\mu }'</math> increases.

Harry Guo: /* Distribution Characteristics */

2012-02-13T19:06:54Z

Distribution Characteristics

← Older revision		Revision as of 19:06, 13 February 2012
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	==Distribution ~~Characteristics~~==		==Characteristics of Lognormal Distribution ==
	[[Image:ldaDC.gif\|thumb\|center\|300px\| ]]		[[Image:ldaDC.gif\|thumb\|center\|300px\| ]]
	<math></math>		<math></math>

Harry Guo: /* Distribution Characteristics */

2012-02-13T19:05:05Z

Distribution Characteristics

← Older revision		Revision as of 19:05, 13 February 2012
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	:• The parameter, <math>{\mu }'</math>, in terms of the logarithm of the <math>{T}'s</math> is also the scale parameter, and not the location parameter as in the case of the normal <math>pdf</math> .		:• The parameter, <math>{\mu }'</math>, in terms of the logarithm of the <math>{T}'s</math> is also the scale parameter, and not the location parameter as in the case of the normal <math>pdf</math> .
	:• The parameter <math>{{\sigma'}}</math>, or the standard deviation of the <math>{T}'s</math> in terms of their logarithm or of their <math>{T}'</math>, is also the shape parameter and not the scale parameter, as in the normal <math>pdf</math>, and assumes only positive values.		:• The parameter <math>{{\sigma'}}</math>, or the standard deviation of the <math>{T}'s</math> in terms of their logarithm or of their <math>{T}'</math>, is also the shape parameter and not the scale parameter, as in the normal <math>pdf</math>, and assumes only positive values.


	'''Lognormal Distribution Parameters in Weibull++'''		'''Lognormal Distribution Parameters in Weibull++'''

	In Weibull++, the parameters returned for the lognormal distribution are always logarithmic. That is: the parameter <math>{\mu }'</math> represents the mean of the natural logarithms of the times-to-failure, while <math>{{\sigma' }}</math> represents the standard deviation of these data point logarithms. Specifically, the returned <math>{{\sigma' }}</math> is the square root of the variance of the natural logarithms of the data points. Even though the application denotes these values as mean and standard deviation, the user is reminded that these are given as the parameters of the distribution, and are thus the mean and standard deviation of the natural logarithms of the data. The mean value of the times-to-failure, not used as a parameter, as well as the standard deviation can be obtained through the QCP or the Function Wizard.		In Weibull++, the parameters returned for the lognormal distribution are always logarithmic. That is: the parameter <math>{\mu }'</math> represents the mean of the natural logarithms of the times-to-failure, while <math>{{\sigma' }}</math> represents the standard deviation of these data point logarithms. Specifically, the returned <math>{{\sigma' }}</math> is the square root of the variance of the natural logarithms of the data points. Even though the application denotes these values as mean and standard deviation, the user is reminded that these are given as the parameters of the distribution, and are thus the mean and standard deviation of the natural logarithms of the data. The mean value of the times-to-failure, not used as a parameter, as well as the standard deviation can be obtained through the QCP or the Function Wizard.

Harry Guo: /* Lognormal Distribution Parameters in Weibull++ */

2012-02-13T19:04:52Z

Lognormal Distribution Parameters in Weibull++

← Older revision		Revision as of 19:04, 13 February 2012
Line 14:		Line 14:
	:• The parameter <math>{{\sigma'}}</math>, or the standard deviation of the <math>{T}'s</math> in terms of their logarithm or of their <math>{T}'</math>, is also the shape parameter and not the scale parameter, as in the normal <math>pdf</math>, and assumes only positive values.		:• The parameter <math>{{\sigma'}}</math>, or the standard deviation of the <math>{T}'s</math> in terms of their logarithm or of their <math>{T}'</math>, is also the shape parameter and not the scale parameter, as in the normal <math>pdf</math>, and assumes only positive values.

	~~===~~Lognormal Distribution Parameters in Weibull++~~===~~		'''Lognormal Distribution Parameters in Weibull++'''

	In Weibull++, the parameters returned for the lognormal distribution are always logarithmic. That is: the parameter <math>{\mu }'</math> represents the mean of the natural logarithms of the times-to-failure, while <math>{{\sigma' }}</math> represents the standard deviation of these data point logarithms. Specifically, the returned <math>{{\sigma' }}</math> is the square root of the variance of the natural logarithms of the data points. Even though the application denotes these values as mean and standard deviation, the user is reminded that these are given as the parameters of the distribution, and are thus the mean and standard deviation of the natural logarithms of the data. The mean value of the times-to-failure, not used as a parameter, as well as the standard deviation can be obtained through the QCP or the Function Wizard.		In Weibull++, the parameters returned for the lognormal distribution are always logarithmic. That is: the parameter <math>{\mu }'</math> represents the mean of the natural logarithms of the times-to-failure, while <math>{{\sigma' }}</math> represents the standard deviation of these data point logarithms. Specifically, the returned <math>{{\sigma' }}</math> is the square root of the variance of the natural logarithms of the data points. Even though the application denotes these values as mean and standard deviation, the user is reminded that these are given as the parameters of the distribution, and are thus the mean and standard deviation of the natural logarithms of the data. The mean value of the times-to-failure, not used as a parameter, as well as the standard deviation can be obtained through the QCP or the Function Wizard.

Harry Guo: /* Distribution Characteristics */

2012-02-13T17:14:41Z

Distribution Characteristics

← Older revision		Revision as of 17:14, 13 February 2012
Line 5:		Line 5:
	:• The lognormal distribution is a distribution skewed to the right.		:• The lognormal distribution is a distribution skewed to the right.
	:• The <math>pdf</math> starts at zero, increases to its mode, and decreases thereafter.		:• The <math>pdf</math> starts at zero, increases to its mode, and decreases thereafter.
	:• The degree of skewness increases as <math>{{\sigma ~~}_{{{T}~~'}}}</math> increases, for a given <math>\mu'</math>		:• The degree of skewness increases as <math>{{\sigma'}}</math> increases, for a given <math>\mu'</math>

	[[Image:ldaDC2.gif\|thumb\|center\|300px\| ]]		[[Image:ldaDC2.gif\|thumb\|center\|300px\| ]]

	:• For the same <math>{{\sigma ~~}_{{{T}~~'}}}</math> , the <math>pdf</math> 's skewness increases as <math>{\mu }'</math> increases.		:• For the same <math>{{\sigma'}}</math> , the <math>pdf</math> 's skewness increases as <math>{\mu }'</math> increases.
	:• For <math>{{\sigma ~~}_{{{T}~~'}}}</math> values significantly greater than 1, the <math>pdf</math> rises very sharply in the beginning, i.e. for very small values of <math>T</math> near zero, and essentially follows the ordinate axis, peaks out early, and then decreases sharply like an exponential <math>pdf</math> or a Weibull <math>pdf</math> with <math>0<\beta <1</math> .		:• For <math>{{\sigma' }}</math> values significantly greater than 1, the <math>pdf</math> rises very sharply in the beginning, i.e. for very small values of <math>T</math> near zero, and essentially follows the ordinate axis, peaks out early, and then decreases sharply like an exponential <math>pdf</math> or a Weibull <math>pdf</math> with <math>0<\beta <1</math> .
	:• The parameter, <math>{\mu }'</math>, in terms of the logarithm of the <math>{T}'s</math> is also the scale parameter, and not the location parameter as in the case of the normal <math>pdf</math> .		:• The parameter, <math>{\mu }'</math>, in terms of the logarithm of the <math>{T}'s</math> is also the scale parameter, and not the location parameter as in the case of the normal <math>pdf</math> .
	:• The parameter <math>{{\sigma ~~}_{{{T}~~'}}}</math>, or the standard deviation of the <math>{T}'s</math> in terms of their logarithm or of their <math>{T}'</math>, is also the shape parameter and not the scale parameter, as in the normal <math>pdf</math>, and assumes only positive values.		:• The parameter <math>{{\sigma'}}</math>, or the standard deviation of the <math>{T}'s</math> in terms of their logarithm or of their <math>{T}'</math>, is also the shape parameter and not the scale parameter, as in the normal <math>pdf</math>, and assumes only positive values.

	===Lognormal Distribution Parameters in Weibull++===		===Lognormal Distribution Parameters in Weibull++===
	In Weibull++, the parameters returned for the lognormal distribution are always logarithmic. That is: the parameter <math>{\mu }'</math> represents the mean of the natural logarithms of the times-to-failure, while <math>{{\sigma ~~}_{{{T}~~'}}}</math> represents the standard deviation of these data point logarithms. Specifically, the returned <math>{{\sigma ~~}_{{{T}~~'}}}</math> is the square root of the variance of the natural logarithms of the data points. Even though the application denotes these values as mean and standard deviation, the user is reminded that these are given as the parameters of the distribution, and are thus the mean and standard deviation of the natural logarithms of the data. The mean value of the times-to-failure, not used as a parameter, as well as the standard deviation can be obtained through the QCP or the Function Wizard.		In Weibull++, the parameters returned for the lognormal distribution are always logarithmic. That is: the parameter <math>{\mu }'</math> represents the mean of the natural logarithms of the times-to-failure, while <math>{{\sigma' }}</math> represents the standard deviation of these data point logarithms. Specifically, the returned <math>{{\sigma' }}</math> is the square root of the variance of the natural logarithms of the data points. Even though the application denotes these values as mean and standard deviation, the user is reminded that these are given as the parameters of the distribution, and are thus the mean and standard deviation of the natural logarithms of the data. The mean value of the times-to-failure, not used as a parameter, as well as the standard deviation can be obtained through the QCP or the Function Wizard.

Harry Guo: moved Template:Ld distribution characteristics to Template:Lognormal distribution characteristics

2012-02-10T23:23:55Z

moved Template:Ld distribution characteristics to Template:Lognormal distribution characteristics

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