Template:Logistic probability paper - Revision history

Richard House: Redirected page to The Logistic Distribution#Logistic Distribution Probability Paper

2012-08-15T01:54:35Z

Redirected page to The Logistic Distribution#Logistic Distribution Probability Paper

← Older revision		Revision as of 01:54, 15 August 2012
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	~~==Logistic Distribution Probability Paper==~~		#REDIRECT [[The_Logistic_Distribution#Logistic_Distribution_Probability_Paper]]
	~~The form of the Logistic probability paper is based on linearizing the <math>cdf</math> .~~
	~~From unreliability equation, <math>z</math> can be calculated as a function of the <math>cdf</math> <math>F</math> as follows:~~

	~~::<math>z=\ln (F)-\ln (1-F)</math>~~

	~~or using the equation for ''z''~~

	~~::<math>\frac{t-\mu }{\sigma }=\ln (F)-\ln (1-F)</math>~~

	~~Then:~~

	~~::<math>\ln (F)-\ln (1-F)=-\frac{\mu }{\sigma }+\frac{1}{\sigma }t</math>~~

	~~Now let:~~

	~~::<math>y=\ln (F)-\ln (1-F)</math>~~

	~~::<math>x=t</math>~~

	~~and:~~

	~~::<math>a=-\frac{\mu }{\sigma }</math>~~

	~~::<math>b=\frac{1}{\sigma }</math>~~

	~~which results in the following linear equation:~~

	~~::<math>y=a+bx</math>~~

	~~The logistic probability paper resulting from this linearized <math>cdf</math> function is shown next.~~

	[[~~Image:WB.14 logistic probability plot.png\|center\|250px\|~~ ]]

	Since the logistic distribution is symmetrical, the area under the <math>pdf</math> curve from <math>-\infty </math> to <math>\mu </math> is <math>0.5</math> , as is the area from <math>\mu </math> to <math>+\infty </math> . Consequently, the value of <math>\mu </math> is said to be the point where <math>R(t)=Q(t)=50%</math> . This means that the estimate of <math>\mu </math> can be read from the point where the plotted line crosses the 50% unreliability line.

	For <math>z=1</math> , <math>\sigma =t-\mu </math> and <math>R(t)=\tfrac{1}{1+\exp (1)}\approx 0.2689.</math> Therefore, <math>\sigma </math> can be found by subtracting <math>\mu </math> from the time value where the plotted probability line crosses the 73.10% unreliability (26.89% reliability) horizontal line.

Nicolette Young: /* Logistic Distribution Probability Paper */

2012-04-25T21:58:03Z

Logistic Distribution Probability Paper

← Older revision		Revision as of 21:58, 25 April 2012
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	The logistic probability paper resulting from this linearized <math>cdf</math> function is shown next.		The logistic probability paper resulting from this linearized <math>cdf</math> function is shown next.

	[[Image:WB.14 logistic probability plot.png\|center\|~~400px~~\| ]]		[[Image:WB.14 logistic probability plot.png\|center\|250px\| ]]

	Since the logistic distribution is symmetrical, the area under the <math>pdf</math> curve from <math>-\infty </math> to <math>\mu </math> is <math>0.5</math> , as is the area from <math>\mu </math> to <math>+\infty </math> . Consequently, the value of <math>\mu </math> is said to be the point where <math>R(t)=Q(t)=50%</math> . This means that the estimate of <math>\mu </math> can be read from the point where the plotted line crosses the 50% unreliability line.		Since the logistic distribution is symmetrical, the area under the <math>pdf</math> curve from <math>-\infty </math> to <math>\mu </math> is <math>0.5</math> , as is the area from <math>\mu </math> to <math>+\infty </math> . Consequently, the value of <math>\mu </math> is said to be the point where <math>R(t)=Q(t)=50%</math> . This means that the estimate of <math>\mu </math> can be read from the point where the plotted line crosses the 50% unreliability line.

	For <math>z=1</math> , <math>\sigma =t-\mu </math> and <math>R(t)=\tfrac{1}{1+\exp (1)}\approx 0.2689.</math> Therefore, <math>\sigma </math> can be found by subtracting <math>\mu </math> from the time value where the plotted probability line crosses the 73.10% unreliability (26.89% reliability) horizontal line.		For <math>z=1</math> , <math>\sigma =t-\mu </math> and <math>R(t)=\tfrac{1}{1+\exp (1)}\approx 0.2689.</math> Therefore, <math>\sigma </math> can be found by subtracting <math>\mu </math> from the time value where the plotted probability line crosses the 73.10% unreliability (26.89% reliability) horizontal line.

Nicolette Young: /* Logistic Distribution Probability Paper */

2012-03-15T17:32:27Z

Logistic Distribution Probability Paper

← Older revision		Revision as of 17:32, 15 March 2012
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	==Logistic Distribution Probability Paper==		==Logistic Distribution Probability Paper==

	The form of the Logistic probability paper is based on linearizing the <math>cdf</math> .		The form of the Logistic probability paper is based on linearizing the <math>cdf</math> .
	From unreliability equation, <math>z</math> can be calculated as a function of the <math>cdf</math> <math>F</math> as follows:		From unreliability equation, <math>z</math> can be calculated as a function of the <math>cdf</math> <math>F</math> as follows:
Line 32:		Line 31:
	The logistic probability paper resulting from this linearized <math>cdf</math> function is shown next.		The logistic probability paper resulting from this linearized <math>cdf</math> function is shown next.

	[[Image:~~ldaLD10~~.4.~~gif\|thumb~~\|center\|400px\| ]]		[[Image:WB.14 logistic probability plot.png\|center\|400px\| ]]

	Since the logistic distribution is symmetrical, the area under the <math>pdf</math> curve from <math>-\infty </math> to <math>\mu </math> is <math>0.5</math> , as is the area from <math>\mu </math> to <math>+\infty </math> . Consequently, the value of <math>\mu </math> is said to be the point where <math>R(t)=Q(t)=50%</math> . This means that the estimate of <math>\mu </math> can be read from the point where the plotted line crosses the 50% unreliability line.		Since the logistic distribution is symmetrical, the area under the <math>pdf</math> curve from <math>-\infty </math> to <math>\mu </math> is <math>0.5</math> , as is the area from <math>\mu </math> to <math>+\infty </math> . Consequently, the value of <math>\mu </math> is said to be the point where <math>R(t)=Q(t)=50%</math> . This means that the estimate of <math>\mu </math> can be read from the point where the plotted line crosses the 50% unreliability line.

	For <math>z=1</math> , <math>\sigma =t-\mu </math> and <math>R(t)=\tfrac{1}{1+\exp (1)}\approx 0.2689.</math> Therefore, <math>\sigma </math> can be found by subtracting <math>\mu </math> from the time value where the plotted probability line crosses the 73.10% unreliability (26.89% reliability) horizontal line.		For <math>z=1</math> , <math>\sigma =t-\mu </math> and <math>R(t)=\tfrac{1}{1+\exp (1)}\approx 0.2689.</math> Therefore, <math>\sigma </math> can be found by subtracting <math>\mu </math> from the time value where the plotted probability line crosses the 73.10% unreliability (26.89% reliability) horizontal line.

Harry Guo: /* Logistic Distribution Probability Paper */

2012-02-14T23:29:49Z

Logistic Distribution Probability Paper

← Older revision		Revision as of 23:29, 14 February 2012
Line 2:		Line 2:

	The form of the Logistic probability paper is based on linearizing the <math>cdf</math> .		The form of the Logistic probability paper is based on linearizing the <math>cdf</math> .
	From ~~Eqn. (UnR fcn)~~, <math>z</math> can be calculated as a function of the <math>cdf</math> <math>F</math> as follows:		From unreliability equation, <math>z</math> can be calculated as a function of the <math>cdf</math> <math>F</math> as follows:

	::<math>z=\ln (F)-\ln (1-F)</math>		::<math>z=\ln (F)-\ln (1-F)</math>

	or using ~~Eqn. (~~z ~~func of parameters)~~		or using the equation for ''z''

	::<math>\frac{T-\mu }{\sigma }=\ln (F)-\ln (1-F)</math>		::<math>\frac{t-\mu }{\sigma }=\ln (F)-\ln (1-F)</math>

	:Then:		Then:

	::<math>\ln (F)-\ln (1-F)=-\frac{\mu }{\sigma }+\frac{1}{\sigma }T</math>		::<math>\ln (F)-\ln (1-F)=-\frac{\mu }{\sigma }+\frac{1}{\sigma }t</math>

	:Now let:		Now let:

	::<math>y=\ln (F)-\ln (1-F)</math>		::<math>y=\ln (F)-\ln (1-F)</math>

	::<math>x=T</math>		::<math>x=t</math>

	:and:		and:

	::<math>a=-\frac{\mu }{\sigma }</math>		::<math>a=-\frac{\mu }{\sigma }</math>

Harry Guo: /* Probability Paper */

2012-02-14T22:45:20Z

Probability Paper

← Older revision		Revision as of 22:45, 14 February 2012
Line 1:		Line 1:
	====Probability Paper====		==Logistic Distribution Probability Paper==

	The form of the Logistic probability paper is based on linearizing the <math>cdf</math> .		The form of the Logistic probability paper is based on linearizing the <math>cdf</math> .
	From Eqn. (UnR fcn), <math>z</math> can be calculated as a function of the <math>cdf</math> <math>F</math> as follows:		From Eqn. (UnR fcn), <math>z</math> can be calculated as a function of the <math>cdf</math> <math>F</math> as follows:

Nicolette Young: Created page with '====Probability Paper==== The form of the Logistic probability paper is based on linearizing the $cdf$ . From Eqn. (UnR fcn), $z$ can be calculated as a…'

2012-01-04T21:58:24Z

Created page with '====Probability Paper==== The form of the Logistic probability paper is based on linearizing the <math>cdf</math> . From Eqn. (UnR fcn), <math>z</math> can be calculated as a…'

New page

====Probability Paper====
The form of the Logistic probability paper is based on linearizing the <math>cdf</math> .
From Eqn. (UnR fcn), <math>z</math> can be calculated as a function of the <math>cdf</math> <math>F</math> as follows:

::<math>z=\ln (F)-\ln (1-F)</math>

or using Eqn. (z func of parameters)

::<math>\frac{T-\mu }{\sigma }=\ln (F)-\ln (1-F)</math>

:Then:

::<math>\ln (F)-\ln (1-F)=-\frac{\mu }{\sigma }+\frac{1}{\sigma }T</math>

:Now let:

::<math>y=\ln (F)-\ln (1-F)</math>

::<math>x=T</math>

:and:

::<math>a=-\frac{\mu }{\sigma }</math>

::<math>b=\frac{1}{\sigma }</math>

which results in the following linear equation:

::<math>y=a+bx</math>

The logistic probability paper resulting from this linearized <math>cdf</math> function is shown next.

[[Image:ldaLD10.4.gif|thumb|center|400px| ]]

Since the logistic distribution is symmetrical, the area under the <math>pdf</math> curve from <math>-\infty </math> to <math>\mu </math> is <math>0.5</math> , as is the area from <math>\mu </math> to <math>+\infty </math> . Consequently, the value of <math>\mu </math> is said to be the point where <math>R(t)=Q(t)=50%</math> . This means that the estimate of <math>\mu </math> can be read from the point where the plotted line crosses the 50% unreliability line.

For <math>z=1</math> , <math>\sigma =t-\mu </math> and <math>R(t)=\tfrac{1}{1+\exp (1)}\approx 0.2689.</math> Therefore, <math>\sigma </math> can be found by subtracting <math>\mu </math> from the time value where the plotted probability line crosses the 73.10% unreliability (26.89% reliability) horizontal line.

Template:Logistic probability paper - Revision history

Richard House: Redirected page to The Logistic Distribution#Logistic Distribution Probability Paper

Nicolette Young: /* Logistic Distribution Probability Paper */

Nicolette Young: /* Logistic Distribution Probability Paper */

Harry Guo: /* Logistic Distribution Probability Paper */

Harry Guo: /* Probability Paper */

Nicolette Young: Created page with '====Probability Paper==== The form of the Logistic probability paper is based on linearizing the cdf . From Eqn. (UnR fcn), z can be calculated as a…'

Nicolette Young: Created page with '====Probability Paper==== The form of the Logistic probability paper is based on linearizing the $cdf$ . From Eqn. (UnR fcn), $z$ can be calculated as a…'