52.2.11 Continuous Uniform Random Variable

The continuous uniform distribution is constant over the interval \([a,b]\) and is zero elsewhere.

Function: pdf_continuous_uniform (x,a,b) ¶

Returns the value at x of the density function of a \({\it ContinuousUniform}(a,b)\) random variable, with \(a<b\). To make use of this function, write first load("distrib").

The pdf

\[f(x; a, b) = \cases{ \displaystyle{1\over b-a} & for $0 \le x \le 1$ \cr \cr 0 & otherwise } \]

and is 0 otherwise.

Categories: Package distrib ·

Function: cdf_continuous_uniform (x,a,b) ¶

Returns the value at x of the distribution function of a \({\it ContinuousUniform}(a,b)\) random variable, with \(a<b\). To make use of this function, write first load("distrib").

The cdf is

\[F(x; a, b) = \cases{ 0 & for $x < a$ \cr \cr \displaystyle{x-a\over b-a} & for $a \le x \le b$ \cr \cr 1 & for $x > b$ } \]

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Function: quantile_continuous_uniform (q,a,b) ¶

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

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Function: mean_continuous_uniform (a,b) ¶

Returns the mean of a \({\it ContinuousUniform}(a,b)\) random variable, with \(a<b\). To make use of this function, write first load("distrib").

The mean is

\[E[X] = {a+b\over 2} \]

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Function: var_continuous_uniform (a,b) ¶

Returns the variance of a \({\it ContinuousUniform}(a,b)\) random variable, with \(a<b\). To make use of this function, write first load("distrib").

The variance is

\[V[X] = {(b-a)^2\over 12} \]

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Function: std_continuous_uniform (a,b) ¶

Returns the standard deviation of a \({\it ContinuousUniform}(a,b)\) random variable, with \(a<b\). To make use of this function, write first load("distrib").

The standard deviation is

\[D[X] = {b-a \over 2\sqrt{3}} \]

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Function: skewness_continuous_uniform (a,b) ¶

Returns the skewness coefficient of a \({\it ContinuousUniform}(a,b)\) random variable, with \(a<b\). To make use of this function, write first load("distrib").

The skewness coefficient is

\[SK[X] = 0 \]

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Function: kurtosis_continuous_uniform (a,b) ¶

Returns the kurtosis coefficient of a \({\it ContinuousUniform}(a,b)\) random variable, with \(a<b\). To make use of this function, write first load("distrib").

The kurtosis coefficient is

\[KU[X] = -{6\over5} \]

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Function: random_continuous_uniform (a,b)
    random_continuous_uniform (a,b,n) ¶

Returns a \({\it ContinuousUniform}(a,b)\) random variate, with \(a<b\). Calling random_continuous_uniform with a third argument n, a random sample of size n 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 ·