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The Geometric distibution is a discrete probability distribution. It is the distribution of the number Bernoulli trials that fail before the first success.
Consider flipping a biased coin where heads occurs with probablity p. Then the probability of k-1 tails in a row followed by heads is given by the \({\it Geometric}(p)\) distribution.
Returns the value at x of the probability function of a \({\it Geometric}(p)\) random variable, with 0 < p \leq 1
The pdf is $$ f(x; p) = p(1-p)^x $$
This is interpreted as the probability of x failures before the first success.
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Returns the value at x of the distribution function of a \({\it Geometric}(p)\) random variable, with 0 < p \leq 1
The cdf is $$ 1-(1-p)^{1 + \lfloor x \rfloor} $$
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Returns the q-quantile of a
\({\it Geometric}(p)\) random variable, with
0 < p <= 1;
in other words, this is the inverse of cdf_geometric.
Argument q must be an element of [0,1].
The probability from which the quantile is derived is defined as p (1 - p)^x. This is interpreted as the probability of x failures before the first success.
load("distrib") loads this function.
Returns the mean of a \({\it Geometric}(p)\) random variable, with 0 < p \leq 1.
The mean is $$ E[X] = {1\over p} - 1 $$
The probability from which the mean is derived is defined as p (1 - p)^x. This is interpreted as the probability of x failures before the first success.
load("distrib") loads this function.
Returns the variance of a \({\it Geometric}(p)\) random variable, with 0 < p \leq 1.
The variance is $$ V[X] = {1-p\over p^2} $$
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Returns the standard deviation of a \({\it Geometric}(p)\) random variable, with 0 < p \leq 1.
$$ D[X] = {\sqrt{1-p} \over p} $$load("distrib") loads this function.
Returns the skewness coefficient of a \({\it Geometric}(p)\) random variable, with 0 < p \leq 1.
The skewness coefficient is $$ SK[X] = {2-p \over \sqrt{1-p}} $$
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Returns the kurtosis coefficient of a geometric random variable \({\it Geometric}(p)\), with 0 < p \leq 1.
The kurtosis coefficient is $$ KU[X] = {p^2-6p+6 \over 1-p} $$
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random_geometric(p) returns one random sample from a
\({\it Geometric}(p)\) distribution, with
0 < p <= 1.
random_geometric(p, n) returns a list of n random samples.
The algorithm is based on simulation of Bernoulli trials.
The probability from which the random sample is derived is defined as p (1 - p)^x. This is interpreted as the probability of x failures before the first success.
load("distrib") loads this function.