The probability plots include:
Minitab estimates the probability (P) that is used to calculate the plot points using the following methods.
Term  Description 

n  Number of observations 
i  Rank of the i^{th} ordered observation x(i), where x(1), x(2),...x(n) are the order statistics, or the data ordered from smallest to largest 
The middle line of the probability plot is constructed using the x and y coordinate calculations in this table.
Distribution  x coordinate  y coordinate 

Smallest extreme value  x  ln(–ln(1 – p)) 
Largest extreme value  x  ln(–ln p) 
Weibull  ln(x)  ln(–ln(1 – p)) 
3parameter Weibull  ln(x – threshold)  ln(–ln(1 – p)) 
Exponential  ln(x)  ln(–ln(1 – p)) 
2parameter exponential  ln(x – threshold)  ln(–ln(1 – p)) 
Normal  x  Φ^{–1}_{norm} 
Lognormal  ln(x)  Φ^{–1}_{norm} 
3parameter lognormal  ln(x – threshold)  Φ^{–1}_{norm} 
Logistic  x  
Loglogistic  ln(x)  
3parameter loglogistic  ln(x – threshold)  
Gamma  x  Φ^{–1}_{gamma} 
3parameter gamma  ln(x – threshold)  Φ^{–1}_{gamma} 
Because the plot points do not depend on any distribution, they are the same (before being transformed) for any probability plot. However, the fitted line differs depending on the parametric distribution chosen.
Term  Description 

p  The estimated probability 
Φ^{1}_{norm}  Value returned for p by the inverse CDF for the standard normal distribution 
Φ^{1}_{gamma}  Value returned for p by the inverse CDF for the incomplete gamma distribution 
ln(x)  The natural log of x 
Percentile is a value on a scale of 100 that indicates the percent of a distribution that is equal to or below that value. 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, λ, and θ taken from the appropriate element of the inverse of the Fisher information matrix.
The formulas used for percentile and variance estimates are as follows:
where z_{p} = ln[–ln(1 – p)], the inverse CDF of the smallest extreme value distribution
where z_{p} = ln[–ln(p)], the inverse CDF of the largest extreme value distribution
where z_{p} = ln[–ln(1 – p)], the inverse CDF of the smallest extreme value distribution
where z_{p} = ln[–ln(1 – p)], the inverse CDF of the smallest extreme value distribution
where z_{p} = the inverse CDF of the normal distribution
where z_{p} = the inverse CDF of the normal distribution
where z_{p} = the inverse CDF of the normal distribution
where z_{p} = ln[p/(1 – p)], the inverse CDF of the logistic distribution
where z_{p} = ln[p/(1 – p)], the inverse CDF of the logistic distribution
where z_{p} = ln[p/(1 – p)], the inverse CDF of the logistic distribution
where is the inverse of the regularized incomplete gamma distribution
where is the inverse of the regularized incomplete gamma distribution
Distribution  Confidence limits 

Smallest extreme value  
Largest extreme value  
Normal  
Logistic  
Weibull  
Exponential  
Lognormal  
Loglogistic  
3parameter Weibull 
If λ < 0:
If λ ≥ 0:

2parameter exponential 
If λ < 0:
If λ ≥ 0:

3parameter lognormal 
If λ < 0:
If λ ≥ 0:

3parameter loglogistic 
If λ < 0:
If λ ≥ 0:

Term  Description 

K_{γ}  The (1 + γ) / 2 percentile of a standard normal distribution 