# TIBCO Statistica® Distribution Fitting

The Distribution Fitting options allow the user to compare the distribution of a variable with a wide variety of theoretical distributions. The user can fit a distribution like Normal, Rectangular, Exponential, Gamma, Lognormal, Chi-square, Weibull, Gompertz, Binomial, Poisson, Geometric, or Bernoulli to the data.

Distribution fitting procedures are useful when the user needs to verify the assumption of normality before using a parametric test. For example, the user may want to use the Kolmogorov-Smirnov test for normality or the Shapiro-Wilks W test to test for normality. Or the user wants to quickly confirm an assumption about a variable's distribution.

Industrial accidents can be thought of as the result of the intersection of a series of unfortunate events. Therefore their frequency tends to be distributed according to the Poisson distribution. Variables like height can be determined by an infinite number of independent random events therefore will be distributed following the normal distribution. Events that are like a coin flip with two results (example: pass/fail) work well with the Bernoulli distribution.

The fit can be evaluated via the Chi-square test or the Kolmogorov-Smirnov one-sample test. The fitting parameters can be controlled. The Lilliefors and Shapiro-Wilks' tests are also supported. In addition, the fit of a particular hypothesized distribution to the empirical distribution can be evaluated in customized histograms (standard or cumulative) with overlaid selected functions; line and bar graphs of expected and observed frequencies, discrepancies and other results.

Other distribution fitting options are available in the Process Analysis module, where the user can compute maximum-likelihood parameter estimates for the Beta, Exponential, Extreme Value (Type I, Gumbel), Gamma, Log-Normal, Rayleigh, and Weibull distributions. Additional facilities to fit predefined or user-defined functions to the data are available in Nonlinear Estimation module.