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# LogisticDistribution

 LogisticDistribution represents a logistic distribution with mean and scale parameter .
• The probability density for value in a logistic distribution is proportional to . »
Probability density function:
Cumulative distribution function:
Mean and variance:
Median:
Probability density function:
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Cumulative distribution function:
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Mean and variance:
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Median:
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 Scope   (6)
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:
Closed form for symbolic order:
Closed form for symbolic order:
Closed form for symbolic order:
Hazard function:
Quantile function:
 Applications   (2)
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:
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