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Distributions of the stats Package

 

Description

Examples

Description

• 

Important: The stats package has been deprecated. Use the superseding package Statistics instead.

• 

The following discrete distributions are available:

binomiald[n,p]

discreteuniform[a,b]

empirical[list_prob]

hypergeometric[N1, N2, n]

negativebinomial[n,p]

poisson[mu]

• 

The following continuous distributions are available:

beta[nu1, nu2]

cauchy[a, b]

chisquare[nu]

exponential[alpha, a]

fratio[nu1, nu2]

gamma[a, b]

laplaced[a, b]

logistic[a, b]

lognormal[mu, sigma]

normald[mu, sigma]

studentst[nu]

uniform[a, b]

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 binomialdn,p distribution (binomial distribution) has the probability density function binomialn,xpx1pnx. 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.

• 

The discreteuniforma&comma;b distribution has a probability density function that is equal to zero if x<a or if b<x, and equal to 1ba&plus;1 otherwise. Constraints: x is an integer, ab

• 

The empirical[list_prob] has its probability density function equal to zero if x<1 or nopslist_prob<x and equal to list_probx otherwise. Constraints: the probabilities must add to 1 exactly.

• 

The hypergeometricN1&comma;N2&comma;n, with N1 equal to the size of the success population, N2 equal to the  size of the failure population and n equal to the sample size, has the probability density function binomialN1&comma;xbinomialN2&comma;nxbinomialN1&plus;N2&comma;n. Constraints: nN1&plus;N2.

• 

The negativebinomialn&comma;p distribution has the probability density function equal to

binomialn&plus;x1&comma;xpn1px

  

Constraints: x is a non-negative integer no greater than n, n is a positive integer, p is a number between 0 and 1.

• 

The poissonμ 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.

• 

The β&nu;1,&nu;2 distribution has the probability density function

1/Beta(nu1, nu2) * x^(nu1-1) * (1-x)^(nu2-1).

  

Constraints: nu1, nu2 are positive integers.

• 

The cauchya&comma;b distribution has the probability density function 1πb1+xa2b2,0<b.

• 

The chisquareν distribution has the probability density function

x^((nu-2)/2) exp(-x/2)/2^(nu/2)/GAMMA(nu/2), x>0, nu>0.

  

Constraint: nu is a positive integer.

• 

The exponentialα,a distribution (exponential distribution) has the probability density function equal to  α&ExponentialE;αxa if ax and equal to zero if x<a. Constraint: alpha is a non-negative real number. Default: a&equals;0.

• 

The frationu1&comma;nu2 distribution has the probability density function

GAMMA( (nu1+nu2)/2)/GAMMA(nu1/2)/GAMMA(nu2/2)*(nu1/nu2)^(nu1/2)*

x^((nu1-2)/2) / ( 1+ (nu1/nu2)*f) ^ ((nu1+nu2)/2), x>0, nu1>0, nu2>0

  

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 γa,b distribution gamma distribution has the probability density function xa1&ExponentialE;xbΓaba,0<x,0<a,0<b. The parameter b, if absent, defaults to the value 1.

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The laplaceda&comma;b distribution has the probability density function 12&ExponentialE;xabb, 0<b. The name laplaced is so chosen to distinguish it from the laplace() function.

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The logistica&comma;b distribution has the probability density function

&ExponentialE;xabb1&plus;&ExponentialE;xab2&comma;0<b

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The lognormalμ,σ has the probability density function

&ExponentialE;lnxμ22σ2x2πσ,0<x

  

The parameter mu has the default value 0 and the parameter sigma has the default value 1. Constraint: sigma cannot be 0. See also the normald distribution.

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The normaldμ,σ distribution has the probability density function

&ExponentialE;xμ22σ22πσ2

  

The parameter mu has the default value 0 and the parameter sigma has the default value 1. Note that sigma is the standard deviation and not the variance. Constraint: sigma must be positive.

• 

The studentstν distribution has the probability density function

GAMMA( (nu+1)/2 )/GAMMA(nu/2)/sqrt(nu*Pi)/(1+t^2/nu)^((nu+1)/2)

  

Constraint: nu is a positive integer.

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The uniforma&comma;b distribution has the probability density function equal to 1ba if a<=x<=b, and to  0 otherwise. The value of b defaults to 1&plus;a. The value of a defaults to 0. Constraint: a<b.

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The weibulla&comma;b distribution has the probability density function

axa1&ExponentialE;xbaba&comma;0<x&comma;0<a&comma;0<b

Examples

Important: The stats package has been deprecated. Use the superseding package Statistics instead.

stats&lsqb;statevalf&comma;pf&comma;poisson&lsqb;3&rsqb;&rsqb;2

0.2240418077

(1)

stats&lsqb;statevalf&comma;icdf&comma;normald&rsqb;0.56

0.1509692155

(2)

stats&lsqb;random&comma;&gamma;&lsqb;3&comma;1&rsqb;&rsqb;3

2.482561473&comma;0.5545542660&comma;2.632923698

(3)

See Also

Statistics

Statistics[Distributions]

stats(deprecated)[random]

stats(deprecated)[statevalf]

 


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