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- Index
Distribution
A distribution is a model for how a set of data is suppose to behave. If describes this behavior in terms of probabilities. From this model it can be determined the probability a value is below a certain value or the probability a value is within a certain range. This model is described in terms of the either the density function or the distribution function of the distribution. These two forms are interchangeable as one can be determined based on the other.
Different physical phenomena produce different distributions. When rolling a 6-sided die, one gets 1 to 6 with equal probability. If one tosses a coin 10 times and counts the number of heads, one gets a number from 0 to 10 following a distribution called the binomial distribution. Potentially every physical could produce a unique distribution. Fortunately, many data sets fit the normal distribution due to it being the limiting distribution of addition and subtraction. Another common distribution is the lognormal distributions due to it being the limiting distribution of multiplication and division. For minimum and maximums there are the smallest extreme value family of distributions (including the Weibull distribution) and largest extreme value family of distributions. However, there are many other distributions that might fit your data. The distributions and family of distributions included in Distribution Analyzer are:
Beta Distribution
Exponential Distribution
Negative Exponential Distribution
Gamma Family of Distributions
Johnson Family of Distributions
Largest Extreme Value Family of Distributions
Loglogistic Family of Distributions
Lognormal Family of Distributions
Normal Distribution
Pearson Family of Distributions
Smallest Extreme Value Family of Distributions
Uniform Distribution
For every distribution there is a transformation that makes data from that distribution fit the normal distribution. Identifying the distribution that fits the data is identical to identifying the transformation that makes the data fit the normal distribution.