User contributions for Nicolette Young

4 January 2012

• 18:2518:25, 4 January 2012 diff hist −2,323 The Lognormal Distribution →Distribution Characteristics
• 18:2118:21, 4 January 2012 diff hist +503 N Template:Lognormal distribution failure rate function Created page with '===The Lognormal Failure Rate Function=== The lognormal failure rate is given by: ::<math>\lambda (T)=\frac{f(T)}{R(T)}=\frac{\tfrac{1}{T\cdot {{\sigma }_{{{T}'}}}\sqrt{2\pi }}…'
• 18:2118:21, 4 January 2012 diff hist −465 Template:Lognormal distribution statistical properties →The Lognormal Failure Rate Function
• 18:2118:21, 4 January 2012 diff hist +450 N Template:Lognormal distribution reliable life Created page with '===The Lognormal Reliable Life=== As there is no closed-form solution for the lognormal reliability equation, no closed-form solution exists for the lognormal reliable life eithe…'
• 18:2118:21, 4 January 2012 diff hist −420 Template:Lognormal distribution statistical properties →The Lognormal Reliable Life
• 18:2018:20, 4 January 2012 diff hist +592 N Template:Lognormal distribution conditional reliability Created page with '===The Lognormal Conditional Reliability=== The lognormal conditional reliability function is given by: ::<math>R(t|T)=\frac{R(T+t)}{R(T)}=\frac{\int_{\text{ln}(T+t)}^{\infty }…'
• 18:2018:20, 4 January 2012 diff hist −552 Template:Lognormal distribution statistical properties →The Lognormal Conditional Reliability
• 18:2018:20, 4 January 2012 diff hist +756 N Template:Lognormal distribution reliability function Created page with '===The Lognormal Reliability Function=== The reliability for a mission of time <math>T</math> , starting at age 0, for the lognormal distribution is determined by: ::<math>R(T…'
• 18:2018:20, 4 January 2012 diff hist −719 Template:Lognormal distribution statistical properties →The Lognormal Reliability Function
• 18:1918:19, 4 January 2012 diff hist +574 N Template:Lognormal distribution standard deviation Created page with '===The Standard Deviation=== The standard deviation of the lognormal distribution, <math>{{\sigma }_{T}}</math> , is given by [18]: ::<math>{{\sigma }_{T}}=\sqrt{\left( {{e}^{…'
• 18:1918:19, 4 January 2012 diff hist −550 Template:Lognormal distribution statistical properties →The Standard Deviation
• 18:1918:19, 4 January 2012 diff hist +161 N Template:Lognormal distribution mode Created page with '===The Mode=== The mode of the lognormal distribution, <math>\tilde{T}</math> , is given by [1]: ::<math>\tilde{T}={{e}^{{\mu }'-\sigma _{{{T}'}}^{2}}}</math>'
• 18:1918:19, 4 January 2012 diff hist −150 Template:Lognormal distribution statistical properties →The Mode
• 18:1818:18, 4 January 2012 diff hist +147 N Template:Lognormal distribution median Created page with '===The Median=== The median of the lognormal distribution, <math>\breve{T}</math> , is given by [18]: ::<math>\breve{T}={{e}^{{{\mu }'}}}</math>'
• 18:1818:18, 4 January 2012 diff hist −134 Template:Lognormal distribution statistical properties →The Median
• 18:1818:18, 4 January 2012 diff hist +466 N Template:Lognormal distribution mean Created page with '===The Mean or MTTF=== The mean of the lognormal distribution, <math>\mu </math> , is given by [18]: ::<math>\mu ={{e}^{{\mu }'+\tfrac{1}{2}\sigma _{{{T}'}}^{2}}}</math> The…'
• 18:1818:18, 4 January 2012 diff hist −455 Template:Lognormal distribution statistical properties →The Mean or MTTF
• 18:1818:18, 4 January 2012 diff hist +3,701 N Template:Lognormal distribution statistical properties Created page with '==Lognormal Statistical Properties== ===The Mean or MTTF=== The mean of the lognormal distribution, <math>\mu </math> , is given by [18]: ::<math>\mu ={{e}^{{\mu }'+\tfrac{1}{…'
• 18:1718:17, 4 January 2012 diff hist −3,662 The Lognormal Distribution →Lognormal Statistical Properties
• 18:1618:16, 4 January 2012 diff hist +1,373 N Template:Lognormal distribution probability density function Created page with '==Lognormal Probability Density Function== The lognormal distribution is a two-parameter distribution with parameters <math>{\mu }'</math> and <math>{{\sigma }_{{{T}'}}}</mat…'
• 18:1618:16, 4 January 2012 diff hist −1,328 The Lognormal Distribution →Lognormal Probability Density Function
• 17:4817:48, 4 January 2012 diff hist +3,161 N Template:Normal distribution bayesian confidence bounds Created page with '==Bayesian Confidence Bounds== ===Bounds on Parameters=== From Chapter 5, we know that the marginal posterior distribution of <math>\mu </math> can be written as: ::<math>\b…'
• 17:4817:48, 4 January 2012 diff hist −3,128 The Normal Distribution →Bayesian Confidence Bounds
• 17:4717:47, 4 January 2012 diff hist +11,131 N Template:Normal Distribution likelihood ratio confidence bounds Created page with '===Likelihood Ratio Confidence Bounds=== ====Bounds on Parameters==== As covered in Chapter 5, the likelihood confidence bounds are calculated by finding values for <math>{{\the…'
• 17:4617:46, 4 January 2012 diff hist −11,090 Template:Normal distribution confidence bounds →Likelihood Ratio Confidence Bounds
• 17:4617:46, 4 January 2012 diff hist +7,446 N Template:Normal Distribution fisher matrix confidence bounds Created page with '===Fisher Matrix Confidence Bounds=== ====Bounds on the Parameters==== The lower and upper bounds on the mean, <math>\widehat{\mu }</math> , are estimated from: ::<math>\begin…'
• 17:4617:46, 4 January 2012 diff hist −7,408 Template:Normal distribution confidence bounds →Fisher Matrix Confidence Bounds
• 17:4517:45, 4 January 2012 diff hist +19,222 N Template:Normal distribution confidence bounds Created page with '=Confidence Bounds== The method used by the application in estimating the different types of confidence bounds for normally distributed data is presented in this section. The com…'
• 17:4517:45, 4 January 2012 diff hist −19,182 The Normal Distribution →Confidence Bounds
• 17:4317:43, 4 January 2012 diff hist +4,033 N Template:Normal distribution maximum likelihood estimation Created page with '===Maximum Likelihood Estimation=== As it was outlined in Chapter 3, maximum likelihood estimation works by developing a likelihood function based on the available data and findi…'
• 17:4217:42, 4 January 2012 diff hist −3,980 Template:Normal distribution estimation of the parameters Replaced content with '==Estimation of the Parameters== {{normal distribution probability plotting}} {{normal distribution rank regression on Y}} {{normal distribution rank regression on X}} {{…'
• 17:4217:42, 4 January 2012 diff hist +4,139 N Template:Normal distribution rank regression on X Created page with '===Rank Regression on X=== As was mentioned previously, performing a rank regression on X requires that a straight line be fitted to a set of data points such that the sum of the…'
• 17:4117:41, 4 January 2012 diff hist −4,095 Template:Normal distribution estimation of the parameters No edit summary
• 17:4017:40, 4 January 2012 diff hist +5,278 Template:Normal distribution rank regression on Y →Rank Regression on Y
• 17:4017:40, 4 January 2012 diff hist −5,279 Template:Normal distribution estimation of the parameters →Example 2
• 17:4017:40, 4 January 2012 diff hist +1,869 N Template:Normal distribution rank regression on Y Created page with '===Rank Regression on Y=== Performing rank regression on Y requires that a straight line be fitted to a set of data points such that the sum of the squares of the vertical deviat…'
• 17:4017:40, 4 January 2012 diff hist −1,825 Template:Normal distribution estimation of the parameters →Rank Regression on Y
• 17:3817:38, 4 January 2012 diff hist +2,326 Template:Normal distribution probability plotting →Probability Plotting
• 17:3817:38, 4 January 2012 diff hist −2,327 Template:Normal distribution estimation of the parameters →Example 1
• 17:3717:37, 4 January 2012 diff hist +2,615 N Template:Normal distribution probability plotting Created page with '====Probability Plotting==== As described before, probability plotting involves plotting the failure times and associated unreliability estimates on specially constructed probabi…'
• 17:3717:37, 4 January 2012 diff hist −2,571 Template:Normal distribution estimation of the parameters →Probability Plotting
• 17:3717:37, 4 January 2012 diff hist +20,302 N Template:Normal distribution estimation of the parameters Created page with '==Estimation of the Parameters== ====Probability Plotting==== As described before, probability plotting involves plotting the failure times and associated unreliability estimate…'
• 17:3617:36, 4 January 2012 diff hist −20,250 The Normal Distribution →Estimation of the Parameters
• 17:3217:32, 4 January 2012 diff hist +3,063 N Template:Characteristics of the normal distribution Created page with '==Characteristics of the Normal Distribution== Some of the specific characteristics of the normal distribution are the following: :• The normal <math>pdf</math> has a mean, …'
• 17:3217:32, 4 January 2012 diff hist −3,017 The Normal Distribution →Characteristics of the Normal Distribution
• 17:2917:29, 4 January 2012 diff hist +393 N Template:Normal failure rate function Created page with '===The Normal Failure Rate Function=== The instantaneous normal failure rate is given by: ::<math>\lambda (T)=\frac{f(T)}{R(T)}=\frac{\tfrac{1}{{{\sigma }_{T}}\sqrt{2\pi }}{{e…'
• 17:2917:29, 4 January 2012 diff hist −361 Template:Normal statistical properties →The Normal Failure Rate Function
• 17:2917:29, 4 January 2012 diff hist +414 N Template:Normal reliable life Created page with '===The Normal Reliable Life=== Since there is no closed-form solution for the normal reliability function, there will also be no closed-form solution for the normal reliable lif…'
• 17:2917:29, 4 January 2012 diff hist −390 Template:Normal statistical properties →The Normal Reliable Life
• 17:2817:28, 4 January 2012 diff hist +585 N Template:Normal conditional reliability function Created page with '===The Normal Conditional Reliability Function=== The normal conditional reliability function is given by: ::<math>R(t|T)=\frac{R(T+t)}{R(T)}=\frac{\int_{T+t}^{\infty }\tfrac{…'