Abstract
A new continuous distribution model is introduced, joining triangular and exponential features, respectively on the left and right side of a hinge point. The cumulative distribution function is derived, as well as the first three moments. Expected values and the Pearson index of skewness are tabulated. A possible step-by-step approach to parameter estimation is outlined. An application to Italian geographical data is given, referring to a set of municipalities classified by population, showing a very satisfactory goodness of fit.
Highlights
The research regarding probability density models is always in progress, since many researchers are interested in finding simple functions, which are able to fit a set of experimental data
One of the most recently developed family of densities, the STSP family proposed by Van Dorp and Kotz (2002a) includes the triangular distribution as a particular case
Moving the hinge point to the right the expected value E(Y ) becomes larger, while the parameter κ√is inversely linked to the expected value
Summary
The research regarding probability density models is always in progress, since many researchers are interested in finding simple (or quite simple) functions, which are able to fit a set of experimental data. We often have to deal with “new” sets of data, and it is always more important to have a large choice of probability models, discrete or continuous, in order to find the best fitting one. The triangular distribution, a very simple and well-known one, has been reconsidered and developed by Johnson (1997), Johnson and Kotz (1999), Van Dorp and Kotz (2002b). One of the most recently developed family of densities, the STSP family proposed by Van Dorp and Kotz (2002a) includes the triangular distribution as a particular case. The new distribution is fitted to a set of Italian population data
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