UniformDistribution

Generate a set of random numbers that are uniformly 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:

Distribution parameters estimation for multivariate uniform distribution:

Estimate the distribution parameters from sample data:

Skewness and kurtosis are constant in any dimensions:

The components of multivariate uniform distribution are uncorrelated:

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:

Different mixed moments for a multivariate uniform distribution:

Closed form for symbolic order:

Mixed central moments:

Closed form for symbolic order:

Mixed factorial moments:

Mixed cumulants:

Closed form for symbolic order:

Hazard function:

Hazard function in two dimensions:

Quantile function:

The marginals of multivariate uniform distribution are uniform distributions:

Find the probability that a randomly chosen point is the left part of the interval:

Find the probability that two randomly selected points on a circle create an angle less than :

Generate a uniform distribution of points on a circle:

Obtain a random number from the inverse CDF of a distribution:

The nozzle of a fountain shoots water at speed and angle varying between and with equal probability. Find the expected horizontal distance where water touches the ground:

The phase angle of a sinusoidal signal is uniformly distributed from to . Find the probability that is between and :

Find the probability that the phase angle is at most :

Find the average value of :

Find the probability that is within one standard deviation from the average value:

Two trains arrive at a station independently and stay for 10 minutes. If the arrival times are uniformly distributed, find the probability the two trains will meet at the station within one hour:

The region where the two trains meet:

Shafts are produced with their diameter following uniform distribution over independently of the production of shaft housings, the inner diameter of which follows uniform distribution over . Given that the optimal difference between the diameters is up to , find the probability that a shaft will fit into a housing:

Show the shafts in blue and holes in pink:

The lifetime of a device has uniform distribution. Find the reliability of the device:

The hazard function increasing in time:

Find the reliability of two such devices in a series:

Find the reliability of two such devices in parallel:

Compare the reliability of both systems for and :

Show a distribution function and its histogram in the same plot:

Compare the PDF to its histogram version:

Compare the CDF to its histogram version:

Parameter influence on the CDF for each :

Uniform distribution is closed under scaling and translation:

Assumption of the sign of the scaling factor or explicit numeric value is required:

Truncation:

Relationships to other distributions:

Sum of uniform random variables follows UniformSumDistribution:

For a defined number of variables:

The mean of uniform variables follows BatesDistribution:

Explicitly compute the PDF:

DiscreteUniformDistribution is the discrete analog of UniformDistribution:

The mean of two uniform random variables follows TriangularDistribution:

Explicitly compute the PDF:

Show using characteristic function:

ExponentialDistribution is the limiting distribution of the where is uniformly distributed:

BetaDistribution is an order distribution of uniformly distributed variables:

ChiSquareDistribution is a transformation of UniformDistribution:

LaplaceDistribution is a transformation of UniformDistribution:

LogisticDistribution is a transformation of UniformDistribution:

UniformDistribution is a special case of VonMisesDistribution:

WeibullDistribution is a transformation of UniformDistribution:

WaringYuleDistribution is a parameter mixture of GeometricDistribution and UniformDistribution:

The copula distribution of two univariate uniform distributions is a two-dimensional uniform distribution:

UniformDistribution is not defined when either min or max is not a real number:

UniformDistribution is not defined when :

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