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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


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