Template:Characteristics of the exponential distribution alta - Revision history

Richard House: Redirected page to Distributions Used in Accelerated Testing#Characteristics of the Exponential Distribution

2012-08-16T01:06:11Z

Redirected page to Distributions Used in Accelerated Testing#Characteristics of the Exponential Distribution

← Older revision		Revision as of 01:06, 16 August 2012
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	~~=== Characteristics ===~~		#REDIRECT [[Distributions_Used_in_Accelerated_Testing#Characteristics_of_the_Exponential_Distribution]]

	The characteristics of the 1-parameter exponential distribution can be exemplified by examining its parameter, lambda (<span class="texhtml">λ<span style="font-family: sans-serif;">)</span></span> and the effect lambda has on the ''pdf'', reliability and failure rate functions.<br>

	~~==== Effects of <span class="texhtml">λ</span> on the ''pdf'' ====~~

	~~<br>~~

	[[~~Image:ALTA4pdf.png\|center\|400px~~]] ~~<br>~~

	~~:*The scale parameter is <math>\tfrac{1}{\lambda }</math> .~~
	:*As <span class="texhtml">λ</span> is decreased in value, the distribution is stretched out to the right, and as <span class="texhtml">λ</span> is increased, the distribution is pushed toward the origin.
	~~:*This distribution has no shape parameter, as it has only one shape (i.e., the exponential). Its only parameter is the failure rate, <span class="texhtml">λ</span> .~~
	:*The distribution starts at <span class="texhtml">''T'' = 0</span> at the level of <span class="texhtml">''f''(''T'' = 0) = λ</span>. It decreases thereafter exponentially and monotonically as <span class="texhtml">''T''</span> increases, and it is convex.
	~~:*As <math>T\to \infty </math> , <math>f(T)\to 0</math>.~~
	~~:*This ''pdf'' can be thought of as a special case of the Weibull ''pdf'' with <span class="texhtml">β = 1</span>.~~

	~~<br> [[Image:ALTA4reliabilityvstimeplot.png\|center\|400px]] <br>~~

	~~==== Effects of <span class="texhtml">λ</span> on the Reliability Function ====~~

	~~:*The 1-parameter exponential reliability function starts at the value of 1 at <span class="texhtml">''T'' = 0</span> . It decreases thereafter monotonically and is convex.~~
	~~:*As <math>T\to \infty </math> , <math>R(T\to \infty )\to 0</math>.~~

	~~==== Effects of <span class="texhtml">λ</span> on the Failure Rate Function ====~~

	~~The failure rate function for the exponential distribution is constant and equal to the parameter <span class="texhtml">λ</span> .~~

	~~<br> [[Image:ALTA4FRvsTP.png\|center\|400px]] <br>~~

Chris Kahn: /* Effects of λ on the Failure Rate Function */

2012-06-25T09:56:11Z

Effects of λ on the Failure Rate Function

← Older revision		Revision as of 09:56, 25 June 2012
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	The failure rate function for the exponential distribution is constant and equal to the parameter <span class="texhtml">λ</span> .		The failure rate function for the exponential distribution is constant and equal to the parameter <span class="texhtml">λ</span> .

	<br> [[Image:ALTA4FRvsTP.png\|center\|~~200px~~]] <br>		<br> [[Image:ALTA4FRvsTP.png\|center\|400px]] <br>

Chris Kahn: /* Effects of λ on the pdf */

2012-06-25T09:56:01Z

Effects of λ on the pdf

← Older revision		Revision as of 09:56, 25 June 2012
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	<br>		<br>

	[[Image:ALTA4pdf.png\|center\|~~200px~~]] <br>		[[Image:ALTA4pdf.png\|center\|400px]] <br>

	:*The scale parameter is <math>\tfrac{1}{\lambda }</math> .		:*The scale parameter is <math>\tfrac{1}{\lambda }</math> .
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	:*This ''pdf'' can be thought of as a special case of the Weibull ''pdf'' with <span class="texhtml">β = 1</span>.		:*This ''pdf'' can be thought of as a special case of the Weibull ''pdf'' with <span class="texhtml">β = 1</span>.

	<br> [[Image:ALTA4reliabilityvstimeplot.png\|center\|~~200px~~]] <br>		<br> [[Image:ALTA4reliabilityvstimeplot.png\|center\|400px]] <br>

	==== Effects of <span class="texhtml">λ</span> on the Reliability Function ====		==== Effects of <span class="texhtml">λ</span> on the Reliability Function ====

Chuck Smith: /* Effects of λ on the Failure Rate Function */

2012-04-26T16:01:53Z

Effects of λ on the Failure Rate Function

← Older revision		Revision as of 16:01, 26 April 2012
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	The failure rate function for the exponential distribution is constant and equal to the parameter <span class="texhtml">λ</span> .		The failure rate function for the exponential distribution is constant and equal to the parameter <span class="texhtml">λ</span> .

	<br> [[Image:ALTA4FRvsTP.png\|center\|~~400px~~]] <br>		<br> [[Image:ALTA4FRvsTP.png\|center\|200px]] <br>

Chuck Smith: /* Effects of λ on the pdf */

2012-04-26T16:01:41Z

Effects of λ on the pdf

← Older revision		Revision as of 16:01, 26 April 2012
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	<br>		<br>

	[[Image:ALTA4pdf.png\|center\|~~400px~~]] <br>		[[Image:ALTA4pdf.png\|center\|200px]] <br>

	:*The scale parameter is <math>\tfrac{1}{\lambda }</math> .		:*The scale parameter is <math>\tfrac{1}{\lambda }</math> .
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	:*This ''pdf'' can be thought of as a special case of the Weibull ''pdf'' with <span class="texhtml">β = 1</span>.		:*This ''pdf'' can be thought of as a special case of the Weibull ''pdf'' with <span class="texhtml">β = 1</span>.

	<br> [[Image:ALTA4reliabilityvstimeplot.png\|center\|~~400px~~]] <br>		<br> [[Image:ALTA4reliabilityvstimeplot.png\|center\|200px]] <br>

	==== Effects of <span class="texhtml">λ</span> on the Reliability Function ====		==== Effects of <span class="texhtml">λ</span> on the Reliability Function ====

Nicolette Young: /* Effects of λ on the Failure Rate Function */

2012-03-20T16:43:57Z

Effects of λ on the Failure Rate Function

← Older revision		Revision as of 16:43, 20 March 2012
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	The failure rate function for the exponential distribution is constant and equal to the parameter <span class="texhtml">λ</span> .		The failure rate function for the exponential distribution is constant and equal to the parameter <span class="texhtml">λ</span> .

	<br> [[Image:ALTA4FRvsTP.~~gif\|thumb~~\|center\|400px]] <br>		<br> [[Image:ALTA4FRvsTP.png\|center\|400px]] <br>

Nicolette Young: /* Effects of λ on the pdf */

2012-03-19T22:32:18Z

Effects of λ on the pdf

← Older revision		Revision as of 22:32, 19 March 2012
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	<br>		<br>

	[[Image:ALTA4pdf.~~gif\|thumb~~\|center\|400px]] <br>		[[Image:ALTA4pdf.png\|center\|400px]] <br>

	:*The scale parameter is <math>\tfrac{1}{\lambda }</math> .		:*The scale parameter is <math>\tfrac{1}{\lambda }</math> .
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	:*This ''pdf'' can be thought of as a special case of the Weibull ''pdf'' with <span class="texhtml">β = 1</span>.		:*This ''pdf'' can be thought of as a special case of the Weibull ''pdf'' with <span class="texhtml">β = 1</span>.

	<br> [[Image:ALTA4reliabilityvstimeplot.~~gif\|thumb~~\|center\|400px]] <br>		<br> [[Image:ALTA4reliabilityvstimeplot.png\|center\|400px]] <br>

	==== Effects of <span class="texhtml">λ</span> on the Reliability Function ====		==== Effects of <span class="texhtml">λ</span> on the Reliability Function ====

Chris Kahn at 23:28, 6 March 2012

2012-03-06T23:28:59Z

← Older revision		Revision as of 23:28, 6 March 2012
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	==== Effects of <span class="texhtml">λ</span> on the Failure Rate Function ====		==== Effects of <span class="texhtml">λ</span> on the Failure Rate Function ====

	The failure rate function for the exponential distribution is constant and ~~it is~~ equal to the parameter <span class="texhtml">λ</span> .		The failure rate function for the exponential distribution is constant and equal to the parameter <span class="texhtml">λ</span> .

	<br> [[Image:ALTA4FRvsTP.gif\|thumb\|center\|400px]] <br>		<br> [[Image:ALTA4FRvsTP.gif\|thumb\|center\|400px]] <br>

Chris Kahn at 22:48, 6 March 2012

2012-03-06T22:48:33Z

← Older revision		Revision as of 22:48, 6 March 2012
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	:*The distribution starts at <span class="texhtml">''T'' = 0</span> at the level of <span class="texhtml">''f''(''T'' = 0) = λ</span>. It decreases thereafter exponentially and monotonically as <span class="texhtml">''T''</span> increases, and it is convex.		:*The distribution starts at <span class="texhtml">''T'' = 0</span> at the level of <span class="texhtml">''f''(''T'' = 0) = λ</span>. It decreases thereafter exponentially and monotonically as <span class="texhtml">''T''</span> increases, and it is convex.
	:*As <math>T\to \infty </math> , <math>f(T)\to 0</math>.		:*As <math>T\to \infty </math> , <math>f(T)\to 0</math>.
	:*This ''pdf'' can be thought of as a special case of the Weibull~~<span class="texhtml"</span>~~ ''pdf'' with <span class="texhtml">β = 1</span>.		:*This ''pdf'' can be thought of as a special case of the Weibull ''pdf'' with <span class="texhtml">β = 1</span>.

	<br> [[Image:ALTA4reliabilityvstimeplot.gif\|thumb\|center\|400px]] <br>		<br> [[Image:ALTA4reliabilityvstimeplot.gif\|thumb\|center\|400px]] <br>

	==== Effects of <span class="texhtml">λ</span> on the Reliability Function ====		==== Effects of <span class="texhtml">λ</span> on the Reliability Function ====

Chris Kahn at 22:47, 6 March 2012

2012-03-06T22:47:10Z

← Older revision		Revision as of 22:47, 6 March 2012
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	=== Characteristics ===		=== Characteristics ===

	The characteristics of the 1-parameter exponential distribution can be exemplified by examining its parameter, lambda (<span class="texhtml">λ<span style="font-family: sans-serif;">)</span></span> and the effect lambda has on the ~~<span class="texhtml">~~''p''~~''d''''f''</span>~~, reliability and failure rate functions.<br>		The characteristics of the 1-parameter exponential distribution can be exemplified by examining its parameter, lambda (<span class="texhtml">λ<span style="font-family: sans-serif;">)</span></span> and the effect lambda has on the ''pdf'', reliability and failure rate functions.<br>

	==== Effects of <span class="texhtml">λ</span> on the ''pdf'' ====		==== Effects of <span class="texhtml">λ</span> on the ''pdf'' ====
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	:*This ''pdf'' can be thought of as a special case of the Weibull<span class="texhtml"</span> ''pdf'' with <span class="texhtml">β = 1</span>.		:*This ''pdf'' can be thought of as a special case of the Weibull<span class="texhtml"</span> ''pdf'' with <span class="texhtml">β = 1</span>.

	<br> [[Image:ALTA4reliabilityvstimeplot.gif\|thumb\|center\|400px]] <br>		<br> [[Image:ALTA4reliabilityvstimeplot.gif\|thumb\|center\|400px]] <br>

	==== Effects of <span class="texhtml">λ</span> on the Reliability Function ====		==== Effects of <span class="texhtml">λ</span> on the Reliability Function ====