DISTRIBUTION Subcommand (PPLOT command)

DISTRIBUTION specifies the distribution type of your data. The default is NORMAL if the subcommand is not specified or is specified without a keyword. If the parameters of the distribution type are not specified, DISTRIBUTION estimates them from the sample data and displays them with the plots.

NORMAL(a,b). Normal distribution. The location parameter a can be any numeric value, while the scale parameter b must be positive. If they are not specified, DISTRIBUTION estimates them from the sample mean and sample standard deviation.

EXPONENTIAL(a). Exponential distribution. The scale parameter a must be positive. If the parameter is not specified, DISTRIBUTION estimates it from the sample mean. Negative observations are not allowed.

WEIBULL(a,b). Weibull distribution. The scale and shape parameters a and b must be positive. If they are not specified, DISTRIBUTION estimates them using the least square method. Negative observations are not allowed.

PARETO(a,b). Pareto distribution. The threshold and shape parameters a and b must be positive. If they are not specified, DISTRIBUTION assumes a equals the minimum observation and estimates b by the maximum likelihood method. Negative observations are not allowed.

LNORMAL(a,b). Lognormal distribution. The scale and shape parameters a and b must be positive. If they are not specified, DISTRIBUTION estimates them from the mean and standard deviation of the natural logarithm of the sample data. Negative observations are not allowed.

BETA(a,b). Beta distribution. The shape1 and shape2 parameters a and b must be positive. If they are not specified, DISTRIBUTION estimates them from the sample mean and sample standard deviation. All observations must be between 0 and 1, inclusive.

GAMMA(a,b). Gamma distribution. The shape and scale parameters a and b must be positive. If they are not specified, DISTRIBUTION estimates them from the sample mean and sample standard deviation. Negative observations are not allowed.

LOGISTIC(a,b). Logistic distribution. LOGISTIC takes a location and a scale parameter (a and b). The scale parameter (b) must be positive. If the parameters are not specified, DISTRIBUTION estimates them from the sample mean and sample standard deviation.

LAPLACE(a,b). Laplace or double exponential distribution. LAPLACE takes a location and a scale parameter (a and b). The scale parameter (b) must be positive. If the parameters are not specified, DISTRIBUTION estimates them from the sample mean and sample standard deviation.

UNIFORM(a,b). Uniform distribution. UNIFORM takes a minimum and a maximum parameter (a and b). Parameter a must be equal to or greater than b. If the parameters are not specified, DISTRIBUTION assumes them from the sample data.

HNORMAL(a). Half-normal distribution. Data are assumed to be location-free or centralized. (Location parameter=0.) You can specify the scale parameter a or let DISTRIBUTION estimate it by using the maximum likelihood method.

CHI(df). Chi-square distribution. You must specify the degrees of freedom (df). Negative observations are not allowed.

STUDENT(df). Student’s t distribution. You must specify the degrees of freedom (df).