Continuous Distribution

EXPONENTIAL

Used to model the amount of time until a specific event occurs or to model the time between the independent events. Example:

• the time until the computer locks up
• the time between arrivals of telephone calls
• the time until a part fails

MATLAB: expocdf(x,1/λ) where mean E(X)=1/λ.

GAMMA f(x;λ,t)

when t is a positive integer, the gamma distribution can be used to model the amount of time one has to waith until the t events has occurred.

MATLAB: gampdf(x,t,1/λ).

CHI-SQUARE

A gamma distribution where λ=0.5 and t= v/2 where v is a positive integer, is called a chi-square distribution with v degree of freedom. Chi-square distribution is used to derived the distribution of the sample variance and is important for goodness-fit-test in statistical analysis.

WEIBULL

Closely related to Exponential.
Apply for problems of reliability and life testing.
Used to model the distribution of time it takesa for objects to fail.

BETA

Can be used to model ran var that takes on value over a bounded interval from 0 to 1.

MULTIVARIATE NORMAL