Template:Exponential Distribution Definition - Revision history

Richard House at 18:20, 24 September 2012

2012-09-24T18:20:06Z

← Older revision		Revision as of 18:20, 24 September 2012
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	::<math>\begin{align}		::<math>\begin{align}
	f(t)=\lambda e^{-\lambda (t-\gamma)}		f(t)=\lambda e^{-\lambda (t-\gamma)}
	\end{align}</math>		\end{align}\,\!</math>

	Where <math> \lambda\,\!</math> is the constant failure rate in failures per unit of measurement (e.g., failures per hour, per cycle, etc.) and <math>\gamma\,\!</math> is the location parameter. In addition, <math>\lambda =\tfrac{1}{m}\,\!</math>, where <math>{m}</math> is the mean time between failures (or to failure).		Where <math> \lambda\,\!</math> is the constant failure rate in failures per unit of measurement (e.g., failures per hour, per cycle, etc.) and <math>\gamma\,\!</math> is the location parameter. In addition, <math>\lambda =\tfrac{1}{m}\,\!</math>, where <math>{m}\,\!</math> is the mean time between failures (or to failure).

	If the location parameter, <math>\gamma\,\!</math>, is assumed to be zero, then the distribution becomes the 1-parameter exponential or:		If the location parameter, <math>\gamma\,\!</math>, is assumed to be zero, then the distribution becomes the 1-parameter exponential or:
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	::<math>\begin{align}		::<math>\begin{align}
	f(t)=\lambda e^{-\lambda t}		f(t)=\lambda e^{-\lambda t}
	\end{align}</math>		\end{align}\,\!</math>

	For a detailed discussion of this distribution, see [[The Exponential Distribution\|The Exponential Distribution]].		For a detailed discussion of this distribution, see [[The Exponential Distribution\|The Exponential Distribution]].

Richard House at 00:23, 22 August 2012

2012-08-22T00:23:57Z

← Older revision		Revision as of 00:23, 22 August 2012
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	\end{align}</math>		\end{align}</math>

	Where <math> \lambda</math> is the constant failure rate in failures per unit of measurement (e.g., failures per hour, per cycle, etc.) and <math>\gamma</math> is the location parameter. In addition, <math>\lambda =\tfrac{1}{m}</math>, where <math>{m}</math> is the mean time between failures (or to failure).		Where <math> \lambda\,\!</math> is the constant failure rate in failures per unit of measurement (e.g., failures per hour, per cycle, etc.) and <math>\gamma\,\!</math> is the location parameter. In addition, <math>\lambda =\tfrac{1}{m}\,\!</math>, where <math>{m}</math> is the mean time between failures (or to failure).

	If the location parameter, <~~span class="texhtml"~~>γ</~~span~~>, is assumed to be zero, then the distribution becomes the 1-parameter exponential or:		If the location parameter, <math>\gamma\,\!</math>, is assumed to be zero, then the distribution becomes the 1-parameter exponential or:

	::<math>\begin{align}		::<math>\begin{align}

Richard House at 01:41, 8 August 2012

2012-08-08T01:41:43Z

← Older revision		Revision as of 01:41, 8 August 2012
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	The exponential distribution is commonly used for components or systems exhibiting a ''constant failure rate''. Due to its simplicity, it has been widely employed, even in cases where it doesn't apply. In its most general case, the 2-parameter exponential distribution is defined by: ~~<br>~~		The exponential distribution is commonly used for components or systems exhibiting a ''constant failure rate''. Due to its simplicity, it has been widely employed, even in cases where it doesn't apply. In its most general case, the 2-parameter exponential distribution is defined by:


	::<math>\begin{align}		::<math>\begin{align}
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	Where <math> \lambda</math> is the constant failure rate in failures per unit of measurement (e.g., failures per hour, per cycle, etc.) and <math>\gamma</math> is the location parameter. In addition, <math>\lambda =\tfrac{1}{m}</math>, where <math>{m}</math> is the mean time between failures (or to failure).		Where <math> \lambda</math> is the constant failure rate in failures per unit of measurement (e.g., failures per hour, per cycle, etc.) and <math>\gamma</math> is the location parameter. In addition, <math>\lambda =\tfrac{1}{m}</math>, where <math>{m}</math> is the mean time between failures (or to failure).

	If the location parameter, <span class="texhtml">γ</span>, is assumed to be zero, then the distribution becomes the 1-parameter exponential or: ~~<br>~~		If the location parameter, <span class="texhtml">γ</span>, is assumed to be zero, then the distribution becomes the 1-parameter exponential or:


	::<math>\begin{align}		::<math>\begin{align}

Lisa Hacker at 03:25, 7 August 2012

2012-08-07T03:25:43Z

← Older revision		Revision as of 03:25, 7 August 2012
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	\end{align}</math>		\end{align}</math>

	<math> \lambda</math> is the constant failure rate in failures per unit of measurement (e.g., failures per hour, per cycle, etc.) and <math>\gamma</math> is the location parameter. In addition, <math>\lambda =\tfrac{1}{m}</math>, where <math>{m}</math> is the mean time between failures (or to failure).		Where <math> \lambda</math> is the constant failure rate in failures per unit of measurement (e.g., failures per hour, per cycle, etc.) and <math>\gamma</math> is the location parameter. In addition, <math>\lambda =\tfrac{1}{m}</math>, where <math>{m}</math> is the mean time between failures (or to failure).

	If the location parameter, <span class="texhtml">γ</span>, is assumed to be zero, then the distribution becomes the 1-parameter exponential or: <br>		If the location parameter, <span class="texhtml">γ</span>, is assumed to be zero, then the distribution becomes the 1-parameter exponential or: <br>

Lisa Hacker at 03:25, 7 August 2012

2012-08-07T03:25:18Z

← Older revision		Revision as of 03:25, 7 August 2012
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	\end{align}</math>		\end{align}</math>

	<math> \lambda</math> is the constant failure rate in failures per unit of measurement (e.g., failures per hour, per cycle, etc.). In addition, <math>\lambda =\tfrac{1}{m}</math>, where <math>{m}</math> is the mean time between failures (or to failure).		<math> \lambda</math> is the constant failure rate in failures per unit of measurement (e.g., failures per hour, per cycle, etc.) and <math>\gamma</math> is the location parameter. In addition, <math>\lambda =\tfrac{1}{m}</math>, where <math>{m}</math> is the mean time between failures (or to failure).

	If the location parameter, <span class="texhtml">γ</span>, is assumed to be zero, then the distribution becomes the 1-parameter exponential or: <br>		If the location parameter, <span class="texhtml">γ</span>, is assumed to be zero, then the distribution becomes the 1-parameter exponential or: <br>

Lisa Hacker at 03:24, 7 August 2012

2012-08-07T03:24:35Z

← Older revision		Revision as of 03:24, 7 August 2012
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	The exponential distribution is commonly used for components or systems exhibiting a ''constant failure rate''. Due to its simplicity, it has been widely employed, even in cases where it doesn't apply. ~~It is defined in~~ its most general case by: <br>		The exponential distribution is commonly used for components or systems exhibiting a ''constant failure rate''. Due to its simplicity, it has been widely employed, even in cases where it doesn't apply. In its most general case, the 2-parameter exponential distribution is defined by: <br>


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	\end{align}</math>		\end{align}</math>

	~~with two parameters, namely <span class="texhtml">λ</span> and <span class="texhtml">γ</span> (this form is also known as the ''2-parameter exponential'').~~ <math> \lambda</math> is the constant failure rate in failures per unit of measurement (e.g., failures per hour, per cycle, etc.). In addition, <math>\lambda =\tfrac{1}{m}</math>, where <math>{m}</math> is the mean time between failures (or to failure).		<math> \lambda</math> is the constant failure rate in failures per unit of measurement (e.g., failures per hour, per cycle, etc.). In addition, <math>\lambda =\tfrac{1}{m}</math>, where <math>{m}</math> is the mean time between failures (or to failure).

	If the location parameter, <span class="texhtml">γ</span>, is assumed to be zero, then the distribution becomes the 1-parameter exponential or: <br>		If the location parameter, <span class="texhtml">γ</span>, is assumed to be zero, then the distribution becomes the 1-parameter exponential or: <br>

Lisa Hacker at 03:23, 7 August 2012

2012-08-07T03:23:48Z

← Older revision		Revision as of 03:23, 7 August 2012
Line 6:		Line 6:
	\end{align}</math>		\end{align}</math>

	with two parameters, namely <span class="texhtml">λ</span> and <span class="texhtml">γ</span> (this form is also known as the ''2-parameter exponential''). <math \lambda</math> is the constant failure rate in failures per unit of measurement (e.g., failures per hour, per cycle, etc.). In addition, <math>\lambda =\tfrac{1}{m}</math>, where <math>{m}</math> is the mean time between failures (or to failure).		with two parameters, namely <span class="texhtml">λ</span> and <span class="texhtml">γ</span> (this form is also known as the ''2-parameter exponential''). <math> \lambda</math> is the constant failure rate in failures per unit of measurement (e.g., failures per hour, per cycle, etc.). In addition, <math>\lambda =\tfrac{1}{m}</math>, where <math>{m}</math> is the mean time between failures (or to failure).

	If the location parameter, <span class="texhtml">γ</span>, is assumed to be zero, then the distribution becomes the 1-parameter exponential or: <br>		If the location parameter, <span class="texhtml">γ</span>, is assumed to be zero, then the distribution becomes the 1-parameter exponential or: <br>

Lisa Hacker at 03:23, 7 August 2012

2012-08-07T03:23:31Z

← Older revision		Revision as of 03:23, 7 August 2012
Line 6:		Line 6:
	\end{align}</math>		\end{align}</math>

	with two parameters, namely <span class="texhtml">λ</span> and <span class="texhtml">γ</span> (this form is also known as the ''2-parameter exponential''). If the location parameter, <span class="texhtml">γ</span>, is assumed to be zero, then the distribution becomes the 1-parameter exponential or: <br>		with two parameters, namely <span class="texhtml">λ</span> and <span class="texhtml">γ</span> (this form is also known as the ''2-parameter exponential''). <math \lambda</math> is the constant failure rate in failures per unit of measurement (e.g., failures per hour, per cycle, etc.). In addition, <math>\lambda =\tfrac{1}{m}</math>, where <math>{m}</math> is the mean time between failures (or to failure).

			If the location parameter, <span class="texhtml">γ</span>, is assumed to be zero, then the distribution becomes the 1-parameter exponential or: <br>

Lisa Hacker at 03:19, 7 August 2012

2012-08-07T03:19:16Z

← Older revision		Revision as of 03:19, 7 August 2012
Line 1:		Line 1:
	The exponential distribution is commonly used for components or systems exhibiting a constant failure rate. It is defined in its most general case by: <br>		The exponential distribution is commonly used for components or systems exhibiting a ''constant failure rate''. Due to its simplicity, it has been widely employed, even in cases where it doesn't apply. It is defined in its most general case by: <br>

Lisa Hacker: Created page with 'The exponential distribution is commonly used for components or systems exhibiting a constant failure rate. It is defined in its most general case by:
:: $\begin{align…'$

2012-08-07T03:17:36Z

Created page with 'The exponential distribution is commonly used for components or systems exhibiting a constant failure rate. It is defined in its most general case by: ::<math>\begin{align…'

New page

The exponential distribution is commonly used for components or systems exhibiting a constant failure rate. It is defined in its most general case by: 

::<math>\begin{align}
f(t)=\lambda e^{-\lambda (t-\gamma)}
\end{align}</math>

with two parameters, namely λ and γ (this form is also known as the ''2-parameter exponential''). If the location parameter, γ, is assumed to be zero, then the distribution becomes the 1-parameter exponential or: 

::<math>\begin{align}
f(t)=\lambda e^{-\lambda t}
\end{align}</math>

For a detailed discussion of this distribution, see [[The Exponential Distribution|The Exponential Distribution]].

Template:Exponential Distribution Definition - Revision history

Richard House at 18:20, 24 September 2012

Richard House at 00:23, 22 August 2012

Richard House at 01:41, 8 August 2012

Lisa Hacker at 03:25, 7 August 2012

Lisa Hacker at 03:25, 7 August 2012

Lisa Hacker at 03:24, 7 August 2012

Lisa Hacker at 03:23, 7 August 2012

Lisa Hacker at 03:23, 7 August 2012

Lisa Hacker at 03:19, 7 August 2012

Lisa Hacker: Created page with 'The exponential distribution is commonly used for components or systems exhibiting a constant failure rate. It is defined in its most general case by: ::\begin{align…'

Lisa Hacker: Created page with 'The exponential distribution is commonly used for components or systems exhibiting a constant failure rate. It is defined in its most general case by:
:: $\begin{align…'$