Discrete Uniform Random Variable (Maxima 5.47.0 Manual)

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 $D i s c r e t e U n i f o r m (1 / 6)$ distribution.

Function: pdf_discrete_uniform (x,n) ¶

Returns the value at x of the probability function of a $D i s c r e t e U n i f o r m (n)$ random variable, with $n$ a strictly positive integer. To make use of this function, write first load("distrib").

The pdf is

$f (x, n) = \frac{1}{n}$

Categories: Package distrib ·

Function: cdf_discrete_uniform (x,n) ¶

Returns the value at x of the distribution function of a $D i s c r e t e U n i f o r m (n)$ random variable, with $n$ a strictly positive integer. To make use of this function, write first load("distrib").

The cdf is

$F (x; n) = \frac{⌊ x ⌋}{n}$

Categories: Package distrib ·

Function: quantile_discrete_uniform (q,n) ¶: Returns the q-quantile of a $D i s c r e t e U n i f o r m (n)$ 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 $D i s c r e t e U n i f o r m (n)$ random variable, with $n$ a strictly positive integer. To make use of this function, write first load("distrib").

The mean is

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

Categories: Package distrib ·

Function: var_discrete_uniform (n) ¶

Returns the variance of a $D i s c r e t e U n i f o r m (n)$ random variable, with $n$ a strictly positive integer. To make use of this function, write first load("distrib").

The variance is

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

Categories: Package distrib ·

Function: std_discrete_uniform (n) ¶

Returns the standard deviation of a $D i s c r e t e U n i f o r m (n)$ random variable, with $n$ a strictly positive integer. To make use of this function, write first load("distrib").

The standard deviation is

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

Categories: Package distrib ·

Function: skewness_discrete_uniform (n) ¶

Returns the skewness coefficient of a $D i s c r e t e U n i f o r m (n)$ random variable, with $n$ a strictly positive integer. To make use of this function, write first load("distrib").

The skewness coefficient is

$S K [X] = 0$

Categories: Package distrib ·

Function: kurtosis_discrete_uniform (n) ¶

Returns the kurtosis coefficient of a $D i s c r e t e U n i f o r m (n)$ random variable, with $n$ a strictly positive integer. To make use of this function, write first load("distrib").

The kurtosis coefficient is

$K U [X] = - \frac{6 (n^{2} + 1)}{5 (n^{2} - 1)}$

Categories: Package distrib ·

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

Returns a $D i s c r e t e U n i f o r m (n)$ 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 ·