Classes Of Distribution

Commonly Used Distributions include Normal, Binomial, Poisson, Chi-square, Student’s t and F distribution.

Normal Distribution:

Has numerous applications. Useful when it is equally likely that readings will fall above or below the average. When a sample of several random measurements is averaged, distribution of such repeated sample averages tends to be normally distributed regardless of the distribution of the measurements being averaged.

Binomial Distribution:

• Used to model discrete data.




• Applies when population is large (N > 50) & when sample size is small compared to population.




• Best applied when sample size is less than 10% of N (n<0.1N).




• Sampling is with replacement. Approximation to hyper-geometric distribution.




• Used to model situations having two possible outcomes.

Poisson Distribution:

• Used to model discrete data




• Used to model rates such as rabbits per acre, defects per unit, or arrivals per hour




• Can be an approximation to binomial distribution when p is equal to or less than 0.1, and sample size is fairly large




• Used as a distribution for defect counts




• Closely related to exponential distribution

Classes of Distributions:

Chi Square Distribution

• Not used to model physical phenomena, like time to fail, etc.




• Used to make decisions and construct confidence intervals.




• This distribution is a special case of gamma distribution with a failure rate of 2, and degrees of freedom equal to 2 divided by the number of degrees of freedom for the corresponding chi square distribution. This is considered a sampling distribution.

F Distribution:

• Not used to model physical phenomena, like time to fail, etc




• Used to make decisions and construct confidence intervals




• Used extensively to test for equality of variances from two normal populations




• This is considered a sampling distribution

Student’s t Distribution:

• Formed by combining standard normal random variable and a chi square random variable.




• Commonly used for hypothesis testing and constructing confidence intervals for means.




• Used in place of normal distribution when standard deviation is unknown.




• If the sample size is large, n>100, the error in the estimated standard deviation is small, and t distribution is approximately normal