LogisticDistribution

Generate a set of pseudorandom numbers that are logistically distributed:

Compare histogram to the PDF:

Distribution parameters estimation:

Estimate the distribution parameters from sample data:

Compare the density histogram of the sample with the PDF of the estimated distribution:

Skewness and kurtosis are constant:

Different moments with closed forms as functions of parameters:

Moment:

Closed form for symbolic order:

CentralMoment:

Closed form for symbolic order:

FactorialMoment:

Cumulant:

Closed form for symbolic order:

Hazard function:

Quantile function:

Logistic distribution can be used to approximate wind speeds:

Find the estimated distribution:

Compare the PDF to the histogram of the wind data:

Find the probability of a day with wind speed greater than 30 km/h:

Find the mean wind speed:

Simulate wind speeds for a month:

Logistic distribution provides a very good fit for fractional price changes from the previous closing price of stocks. Find the estimated distribution for the daily fractional price changes of the Standard & Poor's 500 index from January 1, 2000 to January 1, 2009:

Compare a histogram of the data with the PDF of the estimated distribution:

Find the probability of the fractional price change being greater than 0.5%:

Find the mean fractional price change:

Simulate fractional price changes for 30 days:

Show that using logistic distribution provides better fit than when using LogNormalDistribution:

Parameter influence on the CDF for each :

Logistic distribution is closed under translation and scaling by a positive factor:

The probability density function can be expressed in terms of the square of Sech:

Logistic distribution mimics SechDistribution:

Compare the histogram to the PDF of the estimated distribution:

Comparing the fit with the original distribution:

Relationships to other distributions:

Logistic distribution is a transformation of UniformDistribution:

Logistic distribution is a transformation from ExponentialDistribution:

Logistic distribution is a transformation of ExponentialDistribution:

The difference of two variates from GumbelDistribution follows the same distribution as the difference of two variates from ExtremeValueDistribution, which is logistic distribution:

Sum of ExtremeValueDistribution and GumbelDistribution follows logistic distribution:

LogisticDistribution is not defined when is not a real number:

LogisticDistribution is not defined when is not a positive real number:

Substitution of invalid parameters into symbolic outputs gives results that are not meaningful: