Distributions of the stats Package
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Description
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The following discrete distributions are available:
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binomiald[n,p]
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discreteuniform[a,b]
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empirical[list_prob]
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hypergeometric[N1, N2, n]
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negativebinomial[n,p]
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poisson[mu]
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The following continuous distributions are available:
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beta[nu1, nu2]
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cauchy[a, b]
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chisquare[nu]
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exponential[alpha, a]
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fratio[nu1, nu2]
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gamma[a, b]
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laplaced[a, b]
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logistic[a, b]
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lognormal[mu, sigma]
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normald[mu, sigma]
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studentst[nu]
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uniform[a, b]
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weibull[a, b]
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In the following, the discrete distributions have probability density functions that are evaluated at integral values of x.
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The distribution (binomial distribution) has the probability density function . The name binomiald is so chosen in order to distinguish it from the function binomial(). Constraints: x is a non-negative integer no greater than n, n is a positive integer, p is a number between 0 and 1.
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The distribution has the probability density function equal to
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Constraints: x is a non-negative integer no greater than n, n is a positive integer, p is a number between 0 and 1.
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The distribution has the probability density function exp(-mu)*mu^x/x!
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For the continuous distributions, the parameter x takes a real value.
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The distribution has the probability density function
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1/Beta(nu1, nu2) * x^(nu1-1) * (1-x)^(nu2-1).
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Constraints: nu1, nu2 are positive integers.
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The distribution has the probability density function .
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The distribution has the probability density function
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x^((nu-2)/2) exp(-x/2)/2^(nu/2)/GAMMA(nu/2), x>0, nu>0.
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Constraint: nu is a positive integer.
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The distribution has the probability density function
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GAMMA( (nu1+nu2)/2)/GAMMA(nu1/2)/GAMMA(nu2/2)*(nu1/nu2)^(nu1/2)*
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x^((nu1-2)/2) / ( 1+ (nu1/nu2)*f) ^ ((nu1+nu2)/2), x>0, nu1>0, nu2>0
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This distribution is also known as the Fisher F distribution and the variance ratio distribution. Constraints: nu1, nu2 are positive integers.
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The distribution has the probability density function
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The has the probability density function
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The parameter mu has the default value and the parameter sigma has the default value . Constraint: sigma cannot be 0. See also the normald distribution.
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The distribution has the probability density function
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The parameter mu has the default value and the parameter sigma has the default value . Note that sigma is the standard deviation and not the variance. Constraint: sigma must be positive.
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The distribution has the probability density function
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GAMMA( (nu+1)/2 )/GAMMA(nu/2)/sqrt(nu*Pi)/(1+t^2/nu)^((nu+1)/2)
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Constraint: nu is a positive integer.
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The distribution has the probability density function
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Examples
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Important: The stats package has been deprecated. Use the superseding package Statistics instead.
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