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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