Percentiles are estimates of the times at which a certain percent of the population has failed. By default, Minitab displays tables of percentiles for parametric distribution analysis for common percentiles.
The standard errors for the percentile estimates are the square root of the variances.
, , , , , , , , , , and denote the variances and covariances of the MLEs of μ, σ, α, β, θ, and λ, which are taken from the appropriate element of the inverse of the Fisher information matrix.
The formulas used for percentile and variance estimates for each distribution are as follows:
Term  Description 

z_{p} 
the inverse cdf of the standard distribution evaluated at p (the p^{th} percentile of the standard distribution) 
Distribution  Confidence limits 

Smallest extreme value Normal Logistic 

Weibull Exponential Lognormal Loglogistic 
where (for Weibull distribution) (for exponential distribution) (for lognormal and loglogistic distributions) 
3parameter Weibull 2parameter exponential 3parameter lognormal 3parameter loglogistic 
If λ < 0: If λ 0: where (for 3parameter Weibull distribution) (for 2parameter exponential distribution) (for 3parameter lognormal and loglogistic distributions) 
For the calculations of the variance of the estimated x_{p}, see the section "Percentiles and standard error of percentiles".
Term  Description 

z_{α}  the upper critical value for the standard normal distribution where 100α % is the confidence level. 