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Probability distribution fitting or simply distribution fitting is the fitting of a probability distribution to a series of data concerning the repeated measurement of a variable phenomenon. The aim of distribution fitting is to predict the probability or to forecast the frequency of occurrence of the magnitude of the phenomenon in a certain interval. There are many probability distributions (see list of probability distributions) of which some can be fitted more closely to the observed frequency of the data than others, depending on the characteristics of the phenomenon and of the distribution. The distribution giving a close fit is supposed to lead to good predictions. In distribution fitting, therefore, one needs to select a distribution that suits the data well. == Selection of distribution == The selection of the appropriate distribution depends on the presence or absence of symmetry of the data set with respect to the mean value. ''Symmetrical distributions'' When the data are symmetrically distributed around the mean while the frequency of occurrence of data farther away from the mean diminishes, one may for example select the normal distribution, the logistic distribution, or the Student's t-distribution. The first two are very similar, while the last, with one degree of freedom, has "heavier tails" meaning that the values farther away from the mean occur relatively more often (i.e. the kurtosis is higher). The Cauchy distribution is also symmetric. ''Skew distributions to the right'' When the larger values tend to be farther away from the mean than the smaller values, one has a skew distribution to the right (i.e. there is positive skewness), one may for example select the log-normal distribution (i.e. the log values of the data are normally distributed), the log-logistic distribution (i.e. the log values of the data follow a logistic distribution), the Gumbel distribution, the exponential distribution, the Pareto distribution, the Weibull distribution, or the Fréchet distribution. The last three distributions are bounded to the left. ''Skew distributions to the left'' When the smaller values tend to be farther away from the mean than the larger values, one has a skew distribution to the left (i.e. there is negative skewness), one may for example select the ''square-normal distribution'' (i.e. the normal distribution applied to the square of the data values), the inverted (mirrored) Gumbel distribution, or the Gompertz distribution, which is bounded to the left. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Distribution fitting」の詳細全文を読む スポンサード リンク
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