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# BeniniDistribution

 BeniniDistribution represents a Benini distribution with shape parameters and and scale parameter .
• The probability density for value in a Benini distribution is proportional to for .
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   (7)
Generate a set of pseudorandom numbers that are Benini distributed:
Compare its 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 varies with the shape parameters:
Kurtosis varies with the shape parameters:
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Hazard function:
Quantile function:
 Applications   (2)
BeniniDistribution can be used to model the weight of cats:
Fit a Benini distribution to the data:
Compare the histogram of the data to the PDF of the estimated distribution:
Find the average weight of a cat:
Find the median weight of a cat:
Show that the estimated distribution has a heavy right tail:
Find the probability that a cat weighs at least 3 kg:
Simulate weights for a group of 30 cats:
BeniniDistribution can be used to model losses:
Remove the clear outlier, Andrew, the most destructive hurricane:
Fit a generalized beta distribution into the data:
Compare the histogram of the data with the PDF of the estimated distribution:
Find the probability that a loss caused by a hurricane is over 3 billion dollars:
Find the mean hurricane loss:
Simulate possible losses for the next 30 strong hurricanes:
Since BetaPrimeDistribution can also be used to model the losses, compare the fit:
The fit with BeniniDistribution is slightly better:
Parameter influence on the CDF for each :
Benini distribution is closed under scaling by a positive factor:
The parameter behaves as both scale and location parameter:
Relationships to other distributions:
Benini distribution is a transformation of RayleighDistribution:
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