# Methods and formulas for distribution functions in Distribution Overview Plot (Right Censoring)

## Pdf and cdf

The probability density function (pdf) and cumulative distribution function (cdf) for each reliability distribution are as follows:

pdf
cdf

pdf
cdf

pdf
cdf

pdf
cdf

pdf
cdf

pdf
cdf

pdf
cdf

pdf
cdf

pdf
cdf

pdf
cdf

pdf
cdf

### Notation

TermDescription
μ location parameter
σ scale parameter (Weibull and 3-parameter Weibull)
θ scale parameter (smallest extreme value, exponential, and 2-parameter exponential)
αscale parameter (other distributions)
β shape parameter
λ threshold parameter

## Hazard function

The hazard function provides a measure of the likelihood of failure as a function of how long a unit has survived (the instantaneous failure rate at a particular time, t).

### Notation

TermDescription
f(t) pdf of the chosen distribution
F(t) cdf of the chosen distribution

## Relationships between distributions

When data follow a log-based distributions (Weibull, exponential, lognormal, loglogistic), sometimes calculations are simpler by first taking the log of your data and fitting the corresponding related distribution.