Methods and formulas for percentiles in Parametric Distribution Analysis (Right Censoring)

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:

Smallest extreme value

Weibull

3-parameter Weibull

Exponential

2-parameter exponential

Normal

Lognormal

3-parameter lognormal

Logistic

Loglogistic

3-parameter loglogistic

Notation

Distribution	Confidence limits
Smallest extreme value Normal Logistic
Weibull Exponential Lognormal Loglogistic	where (for Weibull distribution) (for exponential distribution) (for lognormal and loglogistic distributions)
3-parameter Weibull 2-parameter exponential 3-parameter lognormal 3-parameter loglogistic	If λ < 0: If λ 0: where (for 3-parameter Weibull distribution) (for 2-parameter exponential distribution) (for 3-parameter lognormal and loglogistic distributions)

For the calculations of the variance of the estimated x_p, see the section "Percentiles and standard error of percentiles".

Notation

Term	Description
zα	the upper critical value for the standard normal distribution where 100α % is the confidence level.