Template:Ald characteristics - Revision history

Richard House: Redirected page to Distributions Used in Accelerated Testing#The Lognormal Distribution

2012-08-16T03:24:46Z

Redirected page to Distributions Used in Accelerated Testing#The Lognormal Distribution

← Older revision		Revision as of 03:24, 16 August 2012
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	~~===Characteristics===~~		#REDIRECT [[Distributions_Used_in_Accelerated_Testing#The_Lognormal_Distribution]]
	~~:* The lognormal distribution is a distribution skewed to the right.~~
	~~:* The <math>pdf</math> starts at zero, increases to its mode, and decreases thereafter.~~
	~~<br>~~
	[[~~Image:chp4pdf.png\|center\|400px\|''Pdf'' of the lognormal distribution.~~]]
	~~<br>~~
	~~<br>~~
	The characteristics of the lognormal distribution can be exemplified by examining the two parameters, the log-mean <math>({{\overline{T}}^{\prime }})</math> and the log-std (<math>{{\sigma }_{{{T}'}}}</math>), and the effect they have on the <math>pdf</math>.
	~~<br>~~
	~~'''Looking at the Log-Mean''' <math>({{\overline{T}}^{\prime }})</math>~~
	:* The parameter, <math>\bar{{T}'}</math>, or the log-mean life, or the <math>MTT{F}'</math> in terms of the logarithm of the <math>{T}'s</math> is also the scale parameter and a unitless number.
	~~:* For the same <math>{{\sigma }_{{{T}'}}}</math> the <math>pdf</math> 's skewness increases as <math>\bar{{T}'}</math> increases.~~
	~~<br>~~
	~~<br>~~
	~~[[Image:chp4pdf2.png\|center\|400px\|''Pdf'' of the lognormal distribution with different log-mean values.]]~~
	~~<br>~~


	~~====Looking at the Log-STD <math>({{\sigma }_{{{T}'}}})</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>. It is a unitless number and assumes only positive values.
	~~:* The degree of skewness increases as <math>{{\sigma }_{{{T}'}}}</math> increases, for a given <math>\bar{{T}'}</math>.~~
	:* 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>.
	~~<br>~~
	~~[[Image:chp4pdf3.png\|center\|400px\|''Pdf'' of the lognormal distribution with different log-std values.]]~~
	~~<br>~~

Chris Kahn: /* Characteristics */

2012-06-25T10:09:37Z

Characteristics

← Older revision		Revision as of 10:09, 25 June 2012
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	:* 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.
	<br>		<br>
	[[Image:chp4pdf.png\|center\|~~250px~~\|''Pdf'' of the lognormal distribution.]]		[[Image:chp4pdf.png\|center\|400px\|''Pdf'' of the lognormal distribution.]]
	<br>		<br>
	<br>		<br>
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	<br>		<br>
	<br>		<br>
	[[Image:chp4pdf2.png\|center\|~~250px~~\|''Pdf'' of the lognormal distribution with different log-mean values.]]		[[Image:chp4pdf2.png\|center\|400px\|''Pdf'' of the lognormal distribution with different log-mean values.]]
	<br>		<br>

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	:* 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 }_{{{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>.
	<br>		<br>
	[[Image:chp4pdf3.png\|center\|~~250px~~\|''Pdf'' of the lognormal distribution with different log-std values.]]		[[Image:chp4pdf3.png\|center\|400px\|''Pdf'' of the lognormal distribution with different log-std values.]]
	<br>		<br>

Chuck Smith: /* Characteristics */

2012-04-26T16:07:06Z

Characteristics

← Older revision		Revision as of 16:07, 26 April 2012
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	:* 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.
	<br>		<br>
	[[Image:chp4pdf.png\|center\|~~500px~~\|''Pdf'' of the lognormal distribution.]]		[[Image:chp4pdf.png\|center\|250px\|''Pdf'' of the lognormal distribution.]]
	<br>		<br>
	<br>		<br>
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	<br>		<br>
	<br>		<br>
	[[Image:chp4pdf2.png\|center\|~~500px~~\|''Pdf'' of the lognormal distribution with different log-mean values.]]		[[Image:chp4pdf2.png\|center\|250px\|''Pdf'' of the lognormal distribution with different log-mean values.]]
	<br>		<br>

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	:* 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 }_{{{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>.
	<br>		<br>
	[[Image:chp4pdf3.png\|center\|~~500px~~\|''Pdf'' of the lognormal distribution with different log-std values.]]		[[Image:chp4pdf3.png\|center\|250px\|''Pdf'' of the lognormal distribution with different log-std values.]]
	<br>		<br>

Nicolette Young: /* Characteristics */

2012-03-20T17:18:31Z

Characteristics

← Older revision		Revision as of 17:18, 20 March 2012
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	:* 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.
	<br>		<br>
	[[Image:chp4pdf.png\|center\|~~400px~~\|''Pdf'' of the lognormal distribution.]]		[[Image:chp4pdf.png\|center\|500px\|''Pdf'' of the lognormal distribution.]]
	<br>		<br>
	<br>		<br>

Nicolette Young: /* Characteristics */

2012-03-20T17:06:38Z

Characteristics

← Older revision		Revision as of 17:06, 20 March 2012
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	<br>		<br>
	<br>		<br>
	[[Image:chp4pdf2.png\|center\|~~400px~~\|''Pdf'' of the lognormal distribution with different log-mean values.]]		[[Image:chp4pdf2.png\|center\|500px\|''Pdf'' of the lognormal distribution with different log-mean values.]]
	<br>		<br>

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	:* 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 }_{{{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>.
	<br>		<br>
	[[Image:chp4pdf3.png\|center\|~~400px~~\|''Pdf'' of the lognormal distribution with different log-std values.]]		[[Image:chp4pdf3.png\|center\|500px\|''Pdf'' of the lognormal distribution with different log-std values.]]
	<br>		<br>

Nicolette Young: /* Characteristics */

2012-03-20T17:02:08Z

Characteristics

← Older revision		Revision as of 17:02, 20 March 2012
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	:* 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.
	<br>		<br>
	[[Image:chp4pdf.~~gif\|thumb~~\|center\|~~300px~~\|''Pdf'' of the lognormal distribution.]]		[[Image:chp4pdf.png\|center\|400px\|''Pdf'' of the lognormal distribution.]]
	<br>		<br>
	<br>		<br>
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	<br>		<br>
	<br>		<br>
	[[Image:chp4pdf2.~~gif\|thumb~~\|center\|~~300px~~\|''Pdf'' of the lognormal distribution with different log-mean values.]]		[[Image:chp4pdf2.png\|center\|400px\|''Pdf'' of the lognormal distribution with different log-mean values.]]
	<br>		<br>

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	:* 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 }_{{{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>.
	<br>		<br>
	[[Image:chp4pdf3.~~gif\|thumb~~\|center\|~~300px~~\|''Pdf'' of the lognormal distribution with different log-std values.]]		[[Image:chp4pdf3.png\|center\|400px\|''Pdf'' of the lognormal distribution with different log-std values.]]
	<br>		<br>

Chris Kahn: /* Characteristics */

2012-03-07T17:32:55Z

Characteristics

Nicolette Young: Created page with '===Characteristics=== :• The lognormal distribution is a distribution skewed to the right. :• The $pdf$ starts at zero, increases to its mode, and decreases ther…'

2012-01-12T18:53:33Z

Created page with '===Characteristics=== :• The lognormal distribution is a distribution skewed to the right. :• The <math>pdf</math> starts at zero, increases to its mode, and decreases ther…'

New page

===Characteristics===
:• The lognormal distribution is a distribution skewed to the right.
:• The <math>pdf</math> starts at zero, increases to its mode, and decreases thereafter.
 
[[Image:chp4pdf.gif|thumb|center|300px|''Pdf'' of the lognormal distribution.]]
 
 
The characteristics of the lognormal distribution can be exemplified by examining the two parameters, the log-mean, <math>({{\overline{T}}^{\prime }}),</math> and the log-std, <math>({{\sigma }_{{{T}'}}}),</math> and the effect they have on the <math>pdf</math> .
 
Looking at the Log-Mean <math>({{\overline{T}}^{\prime }})</math>
:• The parameter, <math>\bar{{T}'}</math> , or the log-mean life, or the <math>MTT{F}'</math> in terms of the logarithm of the <math>{T}'s</math> is also the scale parameter, and is a unitless number.
:• For the same <math>{{\sigma }_{{{T}'}}}</math> the <math>pdf</math> 's skewness increases as <math>\bar{{T}'}</math> increases.
 
 
[[Image:chp4pdf2.gif|thumb|center|300px|''Pdf'' of the lognormal distribution with different log-mean values.]]
 

====Looking at the Log-STD <math>({{\sigma }_{{{T}'}}})</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> . It is a unitless number and assumes only positive values.
:• The degree of skewness increases as <math>{{\sigma }_{{{T}'}}}</math> increases, for a given <math>\bar{{T}'}</math> .
:• 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> .
 
[[Image:chp4pdf3.gif|thumb|center|300px|''Pdf'' of the lognormal distribution with different log-std values.]]

← Older revision		Revision as of 17:32, 7 March 2012
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	===Characteristics===		===Characteristics===
	:• 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.
	<br>		<br>
	[[Image:chp4pdf.gif\|thumb\|center\|300px\|''Pdf'' of the lognormal distribution.]]		[[Image:chp4pdf.gif\|thumb\|center\|300px\|''Pdf'' of the lognormal distribution.]]
	<br>		<br>
	<br>		<br>
	The characteristics of the lognormal distribution can be exemplified by examining the two parameters, the log-mean, <math>({{\overline{T}}^{\prime }}),</math> and the log-std, <math>({{\sigma }_{{{T}'}}}),</math> and the effect they have on the <math>pdf</math> .		The characteristics of the lognormal distribution can be exemplified by examining the two parameters, the log-mean <math>({{\overline{T}}^{\prime }})</math> and the log-std (<math>{{\sigma }_{{{T}'}}}</math>), and the effect they have on the <math>pdf</math>.
	<br>		<br>
	Looking at the Log-Mean <math>({{\overline{T}}^{\prime }})</math>		'''Looking at the Log-Mean''' <math>({{\overline{T}}^{\prime }})</math>
	:• The parameter, <math>\bar{{T}'}</math> , or the log-mean life, or the <math>MTT{F}'</math> in terms of the logarithm of the <math>{T}'s</math> is also the scale parameter, and is a unitless number.		:* The parameter, <math>\bar{{T}'}</math>, or the log-mean life, or the <math>MTT{F}'</math> in terms of the logarithm of the <math>{T}'s</math> is also the scale parameter and a unitless number.
	:• For the same <math>{{\sigma }_{{{T}'}}}</math> the <math>pdf</math> 's skewness increases as <math>\bar{{T}'}</math> increases.		:* For the same <math>{{\sigma }_{{{T}'}}}</math> the <math>pdf</math> 's skewness increases as <math>\bar{{T}'}</math> increases.
	<br>		<br>
	<br>		<br>
Line 18:		Line 18:

	====Looking at the Log-STD <math>({{\sigma }_{{{T}'}}})</math>====		====Looking at the Log-STD <math>({{\sigma }_{{{T}'}}})</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> . It is a unitless number and assumes only positive values.		:* 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>. It is a unitless number and assumes only positive values.
	:• The degree of skewness increases as <math>{{\sigma }_{{{T}'}}}</math> increases, for a given <math>\bar{{T}'}</math> .		:* The degree of skewness increases as <math>{{\sigma }_{{{T}'}}}</math> increases, for a given <math>\bar{{T}'}</math>.
	:• 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 }_{{{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>.
	<br>		<br>
	[[Image:chp4pdf3.gif\|thumb\|center\|300px\|''Pdf'' of the lognormal distribution with different log-std values.]]		[[Image:chp4pdf3.gif\|thumb\|center\|300px\|''Pdf'' of the lognormal distribution with different log-std values.]]
	<br>		<br>

Template:Ald characteristics - Revision history

Richard House: Redirected page to Distributions Used in Accelerated Testing#The Lognormal Distribution

Chris Kahn: /* Characteristics */

Chuck Smith: /* Characteristics */

Nicolette Young: /* Characteristics */

Nicolette Young: /* Characteristics */

Nicolette Young: /* Characteristics */

Chris Kahn: /* Characteristics */

Nicolette Young: Created page with '===Characteristics=== :• The lognormal distribution is a distribution skewed to the right. :• The pdf starts at zero, increases to its mode, and decreases ther…'

Nicolette Young: Created page with '===Characteristics=== :• The lognormal distribution is a distribution skewed to the right. :• The $pdf$ starts at zero, increases to its mode, and decreases ther…'