52.3.6 Discrete Uniform Random Variable

The Discrete uniform distribution is a discrete probablity distribution where a finite number of values are equally likely to occur. The values are \(1,2,3,...,n\).

For example throwing a fair die of 6 sides numbered 1 through 6 follows a \({\it DiscreteUniform}(1/6)\) distribution.

Function: pdf_discrete_uniform (x,n) ¶

Returns the value at x of the probability function of a \({\it DiscreteUniform}(n)\) random variable, with \(n\) a strictly positive integer. To make use of this function, write first load("distrib").

The pdf is

\[f(x,n) = {1\over n} \]

Categories: Package distrib ·

Function: cdf_discrete_uniform (x,n) ¶

Returns the value at x of the distribution function of a \({\it DiscreteUniform}(n)\) random variable, with \(n\) a strictly positive integer. To make use of this function, write first load("distrib").

The cdf is

\[F(x; n) = {\lfloor x \rfloor \over n} \]

Categories: Package distrib ·

Function: quantile_discrete_uniform (q,n) ¶

Returns the q-quantile of a \({\it DiscreteUniform}(n)\) random variable, with \(n\) a strictly positive integer; in other words, this is the inverse of cdf_discrete_uniform. Argument q must be an element of \([0,1]\). To make use of this function, write first load("distrib").

Categories: Package distrib ·

Function: mean_discrete_uniform (n) ¶

Returns the mean of a \({\it DiscreteUniform}(n)\) random variable, with \(n\) a strictly positive integer. To make use of this function, write first load("distrib").

The mean is

\[E[X] = {n+1\over 2} \]

Categories: Package distrib ·

Function: var_discrete_uniform (n) ¶

Returns the variance of a \({\it DiscreteUniform}(n)\) random variable, with \(n\) a strictly positive integer. To make use of this function, write first load("distrib").

The variance is

\[V[X] = {n^2-1 \over 12} \]

Categories: Package distrib ·

Function: std_discrete_uniform (n) ¶

Returns the standard deviation of a \({\it DiscreteUniform}(n)\) random variable, with \(n\) a strictly positive integer. To make use of this function, write first load("distrib").

The standard deviation is

\[D[X] = {\sqrt{n^2-1} \over 2\sqrt{3}} \]

Categories: Package distrib ·

Function: skewness_discrete_uniform (n) ¶

Returns the skewness coefficient of a \({\it DiscreteUniform}(n)\) random variable, with \(n\) a strictly positive integer. To make use of this function, write first load("distrib").

The skewness coefficient is

\[SK[X] = 0 \]

Categories: Package distrib ·

Function: kurtosis_discrete_uniform (n) ¶

Returns the kurtosis coefficient of a \({\it DiscreteUniform}(n)\) random variable, with \(n\) a strictly positive integer. To make use of this function, write first load("distrib").

The kurtosis coefficient is

\[KU[X] = - {6(n^2+1)\over 5 (n^2-1)} \]

Categories: Package distrib ·

Function: random_discrete_uniform (n)
    random_discrete_uniform (n,m) ¶

Returns a \({\it DiscreteUniform}(n)\) random variate, with \(n\) a strictly positive integer. Calling random_discrete_uniform with a second argument m, a random sample of size m will be simulated.

This is a direct application of the random built-in Maxima function.

See also random. To make use of this function, write first load("distrib").

Categories: Package distrib · Random numbers ·