Module SciPy.stats.distributions

SciPy 0.6.0 API Documentation Generated by Endo, 2007-10-17

Variables
Classes
Functions
Imported Names

Variables

all
```
all = alltrue
```

alpha

alpha = alpha_gen(a = 0.0, name = 'alpha', shapes = 'a', extradoc = """

Alpha distribution

alpha.pdf(x,a) = 1/(x**2*Phi(a)*sqrt(2*pi)) * exp(-1/2 * (a-1/x)**2)
where Phi(alpha) is the normal CDF, x > 0, and a > 0.
""")

anglit

anglit = anglit_gen(a = (-Name('pi') / 4), b = (pi / 4), name = 'anglit', extradoc = """

Anglit distribution

anglit.pdf(x) = sin(2*x+pi/2) = cos(2*x)    for -pi/4 <= x <= pi/4
""")

arcsine

arcsine = arcsine_gen(a = 0.0, b = 1.0, name = 'arcsine', extradoc = """

Arcsine distribution

arcsine.pdf(x) = 1/(pi*sqrt(x*(1-x)))
for 0 < x < 1.
""")

arr
```
arr = asarray
```

bernoulli

bernoulli = bernoulli_gen(b = 1, name = 'bernoulli', shapes = 'pr', extradoc = """

Bernoulli distribution

   1 if binary experiment succeeds, 0 otherwise.  Experiment
   succeeds with probabilty *pr*.

   bernoulli.pmf(k,p) = 1-p  if k = 0
                      = p    if k = 1
   for k = 0,1
""")

beta

beta = beta_gen(a = 0.0, b = 1.0, name = 'beta', shapes = 'a,b', extradoc = """

Beta distribution

beta.pdf(x, a, b) = gamma(a+b)/(gamma(a)*gamma(b)) * x**(a-1) * (1-x)**(b-1)
for 0 < x < 1, a, b > 0.
""")

betaprime

betaprime = betaprime_gen(a = 0.0, b = 500.0, name = 'betaprime', shapes = 'a,b', extradoc = """

Beta prime distribution

betaprime.pdf(x, a, b) = gamma(a+b)/(gamma(a)*gamma(b))
                     * x**(a-1) * (1-x)**(-a-b)
for x > 0, a, b > 0.
""")

binom

binom = binom_gen(name = 'binom', shapes = 'n,pr', extradoc = """

Binomial distribution

   Counts the number of successes in *n* independent
   trials when the probability of success each time is *pr*.

   binom.pmf(k,n,p) = choose(n,k)*p**k*(1-p)**(n-k)
   for k in {0,1,...,n}
""")

boltzmann

boltzmann = boltzmann_gen(name = 'boltzmann', longname = 'A truncated discrete exponential ', shapes = 'lambda_,N', extradoc = """

Boltzmann (Truncated Discrete Exponential)

boltzmann.pmf(k,b,N) = (1-exp(-b))*exp(-b*k)/(1-exp(-b*N))
for k=0,..,N-1
""")

bradford

bradford = bradford_gen(a = 0.0, b = 1.0, name = 'bradford', longname = 'A Bradford', shapes = 'c', extradoc = """

Bradford distribution

bradford.pdf(x,c) = c/(k*(1+c*x))
for 0 < x < 1, c > 0 and k = log(1+c).
""")

burr

burr = burr_gen(a = 0.0, name = 'burr', longname = 'Burr', shapes = 'c,d', extradoc = """

Burr distribution

burr.pdf(x,c,d) = c*d * x**(-c-1) * (1+x**(-c))**(-d-1)
for x > 0.
""")

cauchy

cauchy = cauchy_gen(name = 'cauchy', longname = 'Cauchy', extradoc = """

Cauchy distribution

cauchy.pdf(x) = 1/(pi*(1+x**2))

This is the t distribution with one degree of freedom.
""")

chi

chi = chi_gen(a = 0.0, name = 'chi', shapes = 'df', extradoc = """

Chi distribution

chi.pdf(x,df) = x**(df-1)*exp(-x**2/2)/(2**(df/2-1)*gamma(df/2))
for x > 0.
""")

chi2

chi2 = chi2_gen(a = 0.0, name = 'chi2', longname = 'A chi-squared', shapes = 'df', extradoc = """

Chi-squared distribution

chi2.pdf(x,df) = 1/(2*gamma(df/2)) * (x/2)**(df/2-1) * exp(-x/2)
""")

cosine

cosine = cosine_gen(a = -Name('pi'), b = pi, name = 'cosine', extradoc = """

Cosine distribution (approximation to the normal)

cosine.pdf(x) = 1/(2*pi) * (1+cos(x))
for -pi <= x <= pi.
""")

dgamma

dgamma = dgamma_gen(name = 'dgamma', longname = 'A double gamma', shapes = 'a', extradoc = """

Double gamma distribution

dgamma.pdf(x,a) = 1/(2*gamma(a))*abs(x)**(a-1)*exp(-abs(x))
for a > 0.
""")

dlaplace

dlaplace = dlaplace_gen(a = -Name('inf'), name = 'dlaplace', longname = 'A discrete Laplacian', shapes = 'a', extradoc = """

Discrete Laplacian distribution.

dlapacle.pmf(k,a) = tanh(a/2) * exp(-a*abs(k))
for a > 0.
""")

dweibull

dweibull = dweibull_gen(name = 'dweibull', longname = 'A double Weibull', shapes = 'c', extradoc = """

Double Weibull distribution

dweibull.pdf(x,c) = c/2*abs(x)**(c-1)*exp(-abs(x)**c)
""")

eps
```
eps = numpy.finfo(float).eps
```

erlang

erlang = erlang_gen(a = 0.0, name = 'erlang', longname = 'An Erlang', shapes = 'n', extradoc = """

Erlang distribution (Gamma with integer shape parameter)
""")

errp
```
errp = special.errprint
```

expon

expon = expon_gen(a = 0.0, name = 'expon', longname = 'An exponential', extradoc = """

Exponential distribution

expon.pdf(x) = exp(-x)
for x >= 0.

scale = 1.0 / lambda
""")

exponpow

exponpow = exponpow_gen(a = 0.0, name = 'exponpow', longname = 'An exponential power', shapes = 'b', extradoc = """

Exponential Power distribution

exponpow.pdf(x,b) = b*x**(b-1) * exp(1+x**b - exp(x**b))
for x >= 0, b > 0.
""")

exponweib

exponweib = exponweib_gen(a = 0.0, name = 'exponweib', longname = 'An exponentiated Weibull', shapes = 'a,c', extradoc = """

Exponentiated Weibull distribution

exponweib.pdf(x,a,c) = a*c*(1-exp(-x**c))**(a-1)*exp(-x**c)*x**(c-1)
for x > 0, a, c > 0.
""")

f = f_gen(a = 0.0, name = 'f', longname = 'An F', shapes = 'dfn,dfd', extradoc = """

F distribution

                   df2**(df2/2) * df1**(df1/2) * x**(df1/2-1)
F.pdf(x,df1,df2) = --------------------------------------------
                   (df2+df1*x)**((df1+df2)/2) * B(df1/2, df2/2)
for x > 0.
""")

fatiguelife

fatiguelife = fatiguelife_gen(a = 0.0, name = 'fatiguelife', longname = 'A fatigue-life (Birnbaum-Sanders)', shapes = 'c', extradoc = """

Fatigue-life (Birnbaum-Sanders) distribution

fatiguelife.pdf(x,c) = (x+1)/(2*c*sqrt(2*pi*x**3)) * exp(-(x-1)**2/(2*x*c**2))
for x > 0.
""")

fisk

fisk = fisk_gen(a = 0.0, name = 'fink', longname = 'A funk', shapes = 'c', extradoc = """

Fink distribution.

Burr distribution with d=1.
""")

foldcauchy

foldcauchy = foldcauchy_gen(a = 0.0, name = 'foldcauchy', longname = 'A folded Cauchy', shapes = 'c', extradoc = """

A folded Cauchy distributions

foldcauchy.pdf(x,c) = 1/(pi*(1+(x-c)**2)) + 1/(pi*(1+(x+c)**2))
for x >= 0.
""")

foldnorm

foldnorm = foldnorm_gen(a = 0.0, name = 'foldnorm', longname = 'A folded normal', shapes = 'c', extradoc = """

Folded normal distribution

foldnormal.pdf(x,c) = sqrt(2/pi) * cosh(c*x) * exp(-(x**2+c**2)/2)
for c >= 0.
""")

frechet_l

frechet_l = frechet_l_gen(b = 0.0, name = 'frechet_l', longname = 'A Frechet left', shapes = 'c', extradoc = """

A Frechet (left) distribution (also called Weibull maximum)

frechet_l.pdf(x,c) = c * (-x)**(c-1) * exp(-(-x)**c)
for x < 0, c > 0.
""")

frechet_r

frechet_r = frechet_r_gen(a = 0.0, name = 'frechet_r', longname = 'A Frechet right', shapes = 'c', extradoc = """

A Frechet (right) distribution (also called Weibull minimum)

frechet_r.pdf(x,c) = c*x**(c-1)*exp(-x**c)
for x > 0, c > 0.
""")

gam
```
gam = special.gamma
```

gamma

gamma = gamma_gen(a = 0.0, name = 'gamma', longname = 'A gamma', shapes = 'a', extradoc = """

Gamma distribution

For a = integer, this is the Erlang distribution, and for a=1 it is the
exponential distribution.

gamma.pdf(x,a) = x**(a-1)*exp(-x)/gamma(a)
for x >= 0, a > 0.
""")

gausshyper

gausshyper = gausshyper_gen(a = 0.0, b = 1.0, name = 'gausshyper', longname = 'A Gauss hypergeometric', shapes = 'a,b,c,z', extradoc = """

Gauss hypergeometric distribution

gausshyper.pdf(x,a,b,c,z) = C * x**(a-1) * (1-x)**(b-1) * (1+z*x)**(-c)
for 0 <= x <= 1, a > 0, b > 0, and
C = 1/(B(a,b)F[2,1](c,a;a+b;-z))
""")

genexpon

genexpon = genexpon_gen(a = 0.0, name = 'genexpon', longname = 'A generalized exponential', shapes = 'a,b,c', extradoc = """

Generalized exponential distribution

genexpon.pdf(x,a,b,c) = (a+b*(1-exp(-c*x))) * exp(a*x-b*x+b/c*(1-exp(-c*x)))
for x >= 0, a,b,c > 0.
""")

genextreme

genextreme = genextreme_gen(name = 'genextreme', longname = 'A generalized extreme value', shapes = 'c', extradoc = """

Generalized extreme value (see gumbel_r for c=0)

genextreme.pdf(x,c) = exp(-(1-c*x)**(1/c))*(1-c*x)**(1/c-1)
for x <= 1/c, c > 0
""")

gengamma

gengamma = gengamma_gen(a = 0.0, name = 'gengamma', longname = 'A generalized gamma', shapes = 'a,c', extradoc = """

Generalized gamma distribution

gengamma.pdf(x,a,c) = abs(c)*x**(c*a-1)*exp(-x**c)/gamma(a)
for x > 0, a > 0, and c != 0.
""")

genhalflogistic

genhalflogistic = genhalflogistic_gen(a = 0.0, name = 'genhalflogistic', longname = 'A generalized half-logistic', shapes = 'c', extradoc = """

Generalized half-logistic

genhalflogistic.pdf(x,c) = 2*(1-c*x)**(1/c-1) / (1+(1-c*x)**(1/c))**2
for 0 <= x <= 1/c, and c > 0.
""")

genlogistic

genlogistic = genlogistic_gen(name = 'genlogistic', longname = 'A generalized logistic', shapes = 'c', extradoc = """

Generalized logistic distribution

genlogistic.pdf(x,c) = c*exp(-x) / (1+exp(-x))**(c+1)
for x > 0, c > 0.
""")

genpareto

genpareto = genpareto_gen(a = 0.0, name = 'genpareto', longname = 'A generalized Pareto', shapes = 'c', extradoc = """

Generalized Pareto distribution

genpareto.pdf(x,c) = (1+c*x)**(-1-1/c)
for c != 0, and for x >= 0 for all c, and x < 1/abs(c) for c < 0.
""")

geom

geom = geom_gen(a = 1, name = 'geom', longname = 'A geometric', shapes = 'pr', extradoc = """

Geometric distribution

geom.pmf(k,p) = (1-p)**(k-1)*p
for k >= 1
""")

gilbrat

gilbrat = gilbrat_gen(a = 0.0, name = 'gilbrat', longname = 'A Gilbrat', extradoc = """

Gilbrat distribution

gilbrat.pdf(x) = 1/(x*sqrt(2*pi)) * exp(-1/2*(log(x))**2)
""")

gompertz

gompertz = gompertz_gen(a = 0.0, name = 'gompertz', longname = 'A Gompertz (truncated Gumbel) distribution', shapes = 'c', extradoc = """

Gompertz (truncated Gumbel) distribution

gompertz.pdf(x,c) = c*exp(x) * exp(-c*(exp(x)-1))
for x >= 0, c > 0.
""")

gumbel_l

gumbel_l = gumbel_l_gen(name = 'gumbel_l', longname = 'A left-skewed Gumbel', extradoc = """

Left-skewed Gumbel distribution

gumbel_l.pdf(x) = exp(x - exp(x))
""")

gumbel_r

gumbel_r = gumbel_r_gen(name = 'gumbel_r', longname = 'A (right-skewed) Gumbel', extradoc = """

Right-skewed Gumbel (Log-Weibull, Fisher-Tippett, Gompertz) distribution

gumbel_r.pdf(x) = exp(-(x+exp(-x)))
""")

halfcauchy

halfcauchy = halfcauchy_gen(a = 0.0, name = 'halfcauchy', longname = 'A Half-Cauchy', extradoc = """

Half-Cauchy distribution

halfcauchy.pdf(x) = 2/(pi*(1+x**2))
for x >= 0.
""")

halflogistic

halflogistic = halflogistic_gen(a = 0.0, name = 'halflogistic', longname = 'A half-logistic', extradoc = """

Half-logistic distribution

halflogistic.pdf(x) = 2*exp(-x)/(1+exp(-x))**2 = 1/2*sech(x/2)**2
for x >= 0.
""")

halfnorm

halfnorm = halfnorm_gen(a = 0.0, name = 'halfnorm', longname = 'A half-normal', extradoc = """

Half-normal distribution

halfnorm.pdf(x) = sqrt(2/pi) * exp(-x**2/2)
for x > 0.
""")

hypergeom

hypergeom = hypergeom_gen(name = 'hypergeom', longname = 'A hypergeometric', shapes = 'M,n,N', extradoc = """

Hypergeometric distribution

   Models drawing objects from a bin.
   M is total number of objects, n is total number of Type I objects.
   RV counts number of Type I objects in N drawn without replacement from
   population.

   hypergeom.pmf(k, M, n, N) = choose(n,k)*choose(M-n,N-k)/choose(M,N)
   for N - (M-n) <= k <= min(m,N)
""")

hypsecant

hypsecant = hypsecant_gen(name = 'hypsecant', longname = 'A hyperbolic secant', extradoc = """

Hyperbolic secant distribution

hypsecant.pdf(x) = 1/pi * sech(x)
""")

invgamma

invgamma = invgamma_gen(a = 0.0, name = 'invgamma', longname = 'An inverted gamma', shapes = 'a', extradoc = """

Inverted gamma distribution

invgamma.pdf(x,a) = x**(-a-1)/gamma(a) * exp(-1/x)
for x > 0, a > 0.
""")

invnorm

invnorm = invnorm_gen(a = 0.0, name = 'invnorm', longname = 'An inverse normal', shapes = 'mu', extradoc = """

Inverse normal distribution

invnorm.pdf(x,mu) = 1/sqrt(2*pi*x**3) * exp(-(x-mu)**2/(2*x*mu**2))
for x > 0.
""")

invweibull

invweibull = invweibull_gen(a = 0, name = 'invweibull', longname = 'An inverted Weibull', shapes = 'c', extradoc = """

Inverted Weibull distribution

invweibull.pdf(x,c) = c*x**(-c-1)*exp(-x**(-c))
for x > 0, c > 0.
""")

johnsonsb

johnsonsb = johnsonsb_gen(a = 0.0, b = 1.0, name = 'johnsonb', longname = 'A Johnson SB', shapes = 'a,b', extradoc = """

Johnson SB distribution

johnsonsb.pdf(x,a,b) = b/(x*(1-x)) * phi(a + b*log(x/(1-x)))
for 0 < x < 1 and a,b > 0, and phi is the normal pdf.
""")

johnsonsu

johnsonsu = johnsonsu_gen(name = 'johnsonsu', longname = 'A Johnson SU', shapes = 'a,b', extradoc = """

Johnson SU distribution

johnsonsu.pdf(x,a,b) = b/sqrt(x**2+1) * phi(a + b*log(x+sqrt(x**2+1)))
for all x, a,b > 0, and phi is the normal pdf.
""")

ksone

ksone = ksone_gen(a = 0.0, name = 'ksone', longname = 'Kolmogorov-Smirnov A one-sided test statistic.', shapes = 'n', extradoc = """

General Kolmogorov-Smirnov one-sided test.
""")

kstwobign

kstwobign = kstwobign_gen(a = 0.0, name = 'kstwobign', longname = 'Kolmogorov-Smirnov two-sided (for large N)', extradoc = """

Kolmogorov-Smirnov two-sided test for large N
""")

laplace

laplace = laplace_gen(name = 'laplace', longname = 'A Laplace', extradoc = """

Laplacian distribution

laplace.pdf(x) = 1/2*exp(-abs(x))
""")

levy

levy = levy_gen(a = 0.0, name = 'levy', longname = 'A Levy', extradoc = """

Levy distribution

levy.pdf(x) = 1/(x*sqrt(2*pi*x)) * exp(-1/(2*x))
for x > 0.

This is the same as the Levy-stable distribution with a=1/2 and b=1.
""")

levy_l

levy_l = levy_l_gen(b = 0.0, name = 'levy_l', longname = 'A left-skewed Levy', extradoc = """

Left-skewed Levy distribution

levy_l.pdf(x) = 1/(abs(x)*sqrt(2*pi*abs(x))) * exp(-1/(2*abs(x)))
for x < 0.

This is the same as the Levy-stable distribution with a=1/2 and b=-1.
""")

levy_stable

levy_stable = levy_stable_gen(name = 'levy_stable', longname = 'A Levy-stable', shapes = 'alpha, beta', extradoc = """

Levy-stable distribution (only random variates available -- ignore other docs)
""")

loggamma

loggamma = loggamma_gen(name = 'loggamma', longname = 'A log gamma', extradoc = """

Log gamma distribution

loggamma.pdf(x,c) = exp(c*x-exp(x)) / gamma(c)
for all x, c > 0.
""")

logistic

logistic = logistic_gen(name = 'logistic', longname = 'A logistic', extradoc = """

Logistic distribution

logistic.pdf(x) = exp(-x)/(1+exp(-x))**2
""")

loglaplace

loglaplace = loglaplace_gen(a = 0.0, name = 'loglaplace', longname = 'A log-Laplace', shapes = 'c', extradoc = """

Log-Laplace distribution (Log Double Exponential)

loglaplace.pdf(x,c) = c/2*x**(c-1) for 0 < x < 1
                    = c/2*x**(-c-1) for x >= 1
for c > 0.
""")

lognorm

lognorm = lognorm_gen(a = 0.0, name = 'lognorm', longname = 'A lognormal', shapes = 's', extradoc = """

Lognormal distribution

lognorm.pdf(x,s) = 1/(s*x*sqrt(2*pi)) * exp(-1/2*(log(x)/s)**2)
for x > 0, s > 0.
""")

logser

logser = logser_gen(a = 1, name = 'logser', longname = 'A logarithmic', shapes = 'pr', extradoc = """

Logarithmic (Log-Series, Series) distribution

logser.pmf(k,p) = - p**k / (k*log(1-p))
for k >= 1
""")

lomax

lomax = lomax_gen(a = 0.0, name = 'lomax', longname = 'A Lomax (Pareto of the second kind)', shapes = 'c', extradoc = """

Lomax (Pareto of the second kind) distribution

lomax.pdf(x,c) = c / (1+x)**(c+1)
for x >= 0, c > 0.
""")

maxwell

maxwell = maxwell_gen(a = 0.0, name = 'maxwell', longname = 'A Maxwell', extradoc = """

Maxwell distribution

maxwell.pdf(x) = sqrt(2/pi) * x**2 * exp(-x**2/2)
for x > 0.
""")

mielke

mielke = mielke_gen(a = 0.0, name = 'mielke', longname = "A Mielke's Beta-Kappa", shapes = 'k,s', extradoc = """

Mielke's Beta-Kappa distribution

mielke.pdf(x,k,s) = k*x**(k-1) / (1+x**s)**(1+k/s)
for x > 0.
""")

nakagami

nakagami = nakagami_gen(a = 0.0, name = 'nakagami', longname = 'A Nakagami', shapes = 'nu', extradoc = """

Nakagami distribution

nakagami.pdf(x,nu) = 2*nu**nu/gamma(nu) * x**(2*nu-1) * exp(-nu*x**2)
for x > 0, nu > 0.
""")

nbinom

nbinom = nbinom_gen(name = 'nbinom', longname = 'A negative binomial', shapes = 'n,pr', extradoc = """

Negative binomial distribution

nbinom.pmf(k,n,p) = choose(k+n-1,n-1) * p**n * (1-p)**k
for k >= 0.
""")

ncf

ncf = ncf_gen(a = 0.0, name = 'ncf', longname = 'A non-central F distribution', shapes = 'dfn,dfd,nc', extradoc = """

Non-central F distribution

ncf.pdf(x,df1,df2,nc) = exp(nc/2 + nc*df1*x/(2*(df1*x+df2)))
                * df1**(df1/2) * df2**(df2/2) * x**(df1/2-1)
                * (df2+df1*x)**(-(df1+df2)/2)
                * gamma(df1/2)*gamma(1+df2/2)
                * L^{v1/2-1}^{v2/2}(-nc*v1*x/(2*(v1*x+v2)))
                / (B(v1/2, v2/2) * gamma((v1+v2)/2))
for df1, df2, nc > 0.
""")

nct

nct = nct_gen(name = 'nct', longname = 'A Noncentral T', shapes = 'df,nc', extradoc = """

Non-central Student T distribution

                                 df**(df/2) * gamma(df+1)
nct.pdf(x,df,nc) = --------------------------------------------------
                   2**df*exp(nc**2/2)*(df+x**2)**(df/2) * gamma(df/2)
for df > 0, nc > 0.
""")

ncx2

ncx2 = ncx2_gen(a = 0.0, name = 'ncx2', longname = 'A non-central chi-squared', shapes = 'df,nc', extradoc = """

Non-central chi-squared distribution

ncx2.pdf(x,df,nc) = exp(-(nc+df)/2)*1/2*(x/nc)**((df-2)/4)
                        * I[(df-2)/2](sqrt(nc*x))
for x > 0.
""")

norm

norm = norm_gen(name = 'norm', longname = 'A normal', extradoc = """

Normal distribution

The location (loc) keyword specifies the mean.
The scale (scale) keyword specifies the standard deviation.

normal.pdf(x) = exp(-x**2/2)/sqrt(2*pi)
""")

pareto

pareto = pareto_gen(a = 1.0, name = 'pareto', longname = 'A Pareto', shapes = 'b', extradoc = """

Pareto distribution

pareto.pdf(x,b) = b/x**(b+1)
for x >= 1, b > 0.
""")

permutation
```
permutation = mtrand.permutation
```

planck

planck = planck_gen(name = 'planck', longname = 'A discrete exponential ', shapes = 'lambda_', extradoc = """

Planck (Discrete Exponential)

planck.pmf(k,b) = (1-exp(-b))*exp(-b*k)
for k*b >= 0
""")

poisson

poisson = poisson_gen(name = 'poisson', longname = 'A Poisson', shapes = 'mu', extradoc = """

Poisson distribution

poisson.pmf(k, mu) = exp(-mu) * mu**k / k!
for k >= 0
""")

powerlaw

powerlaw = powerlaw_gen(a = 0.0, b = 1.0, name = 'powerlaw', longname = 'A power-function', shapes = 'a', extradoc = """

Power-function distribution

powerlaw.pdf(x,a) = a**x**(a-1)
for 0 <= x <= 1, a > 0.
""")

powerlognorm

powerlognorm = powerlognorm_gen(a = 0.0, name = 'powerlognorm', longname = 'A power log-normal', shapes = 'c,s', extradoc = """

Power log-normal distribution

powerlognorm.pdf(x,c,s) = c/(x*s) * phi(log(x)/s) * (Phi(-log(x)/s))**(c-1)
where phi is the normal pdf, and Phi is the normal cdf, and x > 0, s,c > 0.
""")

powernorm

powernorm = powernorm_gen(name = 'powernorm', longname = 'A power normal', shapes = 'c', extradoc = """

Power normal distribution

powernorm.pdf(x,c) = c * phi(x)*(Phi(-x))**(c-1)
where phi is the normal pdf, and Phi is the normal cdf, and x > 0, c > 0.
""")

rand
```
rand = mtrand.rand
```

randint

randint = randint_gen(name = 'randint', longname = 'A discrete uniform (random integer)', shapes = 'min,max', extradoc = """

Discrete Uniform

    Random integers >=min and <max.

    randint.pmf(k,min, max) = 1/(max-min)
    for min <= k < max.
""")

random
```
random = mtrand.random_sample
```

random_integers

random_integers = mtrand.random_integers

rayleigh

rayleigh = rayleigh_gen(a = 0.0, name = 'rayleigh', longname = 'A Rayleigh', extradoc = """

Rayleigh distribution

rayleigh.pdf(r) = r * exp(-r**2/2)
for x >= 0.
""")

rdist

rdist = rdist_gen(a = -Const(1.0), b = 1.0, name = 'rdist', longname = 'An R-distributed', shapes = 'c', extradoc = """

R-distribution

rdist.pdf(x,c) = (1-x**2)**(c/2-1) / B(1/2, c/2)
for -1 <= x <= 1, c > 0.
""")

recipinvgauss

recipinvgauss = recipinvgauss_gen(a = 0.0, name = 'recipinvgauss', longname = 'A reciprocal inverse Gaussian', shapes = 'mu', extradoc = """

Reciprocal inverse Gaussian

recipinvgauss.pdf(x, mu) = 1/sqrt(2*pi*x**3) * exp(-(x-mu)**2/(2*x*mu**2))
for x >= 0.
""")

reciprocal

reciprocal = reciprocal_gen(name = 'reciprocal', longname = 'A reciprocal', shapes = 'a,b', extradoc = """

Reciprocal distribution

reciprocal.pdf(x,a,b) = 1/(x*log(b/a))
for a <= x <= b, a,b > 0.
""")

rice

rice = rice_gen(a = 0.0, name = 'rice', longname = 'A Rice', shapes = 'b', extradoc = """

Rician distribution

rice.pdf(x,b) = x * exp(-(x**2+b**2)/2) * I[0](x*b)
for x > 0, b > 0.
""")

semicircular

semicircular = semicircular_gen(a = -Const(1.0), b = 1.0, name = 'semicircular', longname = 'A semicircular', extradoc = """

Semicircular distribution

semicircular.pdf(x) = 2/pi * sqrt(1-x**2)
for -1 <= x <= 1.
""")

sgf
```
sgf = vectorize
```

t = t_gen(name = 't', longname = "Student's T", shapes = 'df', extradoc = """

Student's T distribution

                            gamma((df+1)/2)
t.pdf(x,df) = -----------------------------------------------
              sqrt(pi*df)*gamma(df/2)*(1+x**2/df)**((df+1)/2)
for df > 0.
""")

triang

triang = triang_gen(a = 0.0, b = 1.0, name = 'triang', longname = 'A Triangular', shapes = 'c', extradoc = """

Triangular distribution

    up-sloping line from loc to (loc + c*scale) and then downsloping
    for (loc + c*scale) to (loc+scale).

    - standard form is in the range [0,1] with c the mode.
    - location parameter shifts the start to loc
    - scale changes the width from 1 to scale
""")

truncexpon

truncexpon = truncexpon_gen(a = 0.0, name = 'truncexpon', longname = 'A truncated exponential', shapes = 'b', extradoc = """

Truncated exponential distribution

truncexpon.pdf(x,b) = exp(-x)/(1-exp(-b))
for 0 < x < b.
""")

truncnorm

truncnorm = truncnorm_gen(name = 'truncnorm', longname = 'A truncated normal', shapes = 'a,b', extradoc = """

Truncated Normal distribution.

  The standard form of this distribution is a standard normal truncated to the
  range [a,b] --- notice that a and b are defined over the domain
  of the standard normal.  To convert clip values for a specific mean and
  standard deviation use a,b = (myclip_a-my_mean)/my_std, (myclip_b-my_mean)/my_std
""")

tukeylambda

tukeylambda = tukeylambda_gen(name = 'tukeylambda', longname = 'A Tukey-Lambda', shapes = 'lam', extradoc = """

Tukey-Lambda distribution

   A flexible distribution ranging from Cauchy (lam=-1)
   to logistic (lam=0.0)
   to approx Normal (lam=0.14)
   to u-shape (lam = 0.5)
   to Uniform from -1 to 1 (lam = 1)
""")

uniform

uniform = uniform_gen(a = 0.0, b = 1.0, name = 'uniform', longname = 'A uniform', extradoc = """

Uniform distribution

   constant between loc and loc+scale
""")

vonmises

vonmises = vonmises_gen(name = 'vonmises', longname = 'A Von Mises', shapes = 'b', extradoc = """

Von Mises distribution

  if x is not in range or loc is not in range it assumes they are angles
     and converts them to [-pi, pi] equivalents.

  vonmises.pdf(x,b) = exp(b*cos(x)) / (2*pi*I[0](b))
  for -pi <= x <= pi, b > 0.

""")

wald

wald = wald_gen(a = 0.0, name = 'wald', longname = 'A Wald', extradoc = """

Wald distribution

wald.pdf(x) = 1/sqrt(2*pi*x**3) * exp(-(x-1)**2/(2*x))
for x > 0.
""")

weibull_max

weibull_max = frechet_l_gen(b = 0.0, name = 'weibull_max', longname = 'A Weibull maximum', shapes = 'c', extradoc = """

A Weibull maximum distribution (also called a Frechet (left) distribution)

weibull_max.pdf(x,c) = c * (-x)**(c-1) * exp(-(-x)**c)
for x < 0, c > 0.
""")

weibull_min

weibull_min = frechet_r_gen(a = 0.0, name = 'weibull_min', longname = 'A Weibull minimum', shapes = 'c', extradoc = """

A Weibull minimum distribution (also called a Frechet (right) distribution)

weibull_min.pdf(x,c) = c*x**(c-1)*exp(-x**c)
for x > 0, c > 0.
""")

wrapcauchy

wrapcauchy = wrapcauchy_gen(a = 0.0, b = (2 * pi), name = 'wrapcauchy', longname = 'A wrapped Cauchy', shapes = 'c', extradoc = """

Wrapped Cauchy distribution

wrapcauchy.pdf(x,c) = (1-c**2) / (2*pi*(1+c**2-2*c*cos(x)))
for 0 <= x <= 2*pi, 0 < c < 1.
""")

zipf

zipf = zipf_gen(a = 1, name = 'zipf', longname = 'A Zipf', shapes = 'a', extradoc = """

Zipf distribution

zipf.pmf(k,a) = 1/(zeta(a)*k**a)
for k >= 1
""")

Classes

alpha_gen
anglit_gen
arcsine_gen
bernoulli_gen
beta_gen
betaprime_gen
binom_gen
boltzmann_gen
bradford_gen
burr_gen
cauchy_gen
chi2_gen
chi_gen
cosine_gen
dgamma_gen
dlaplace_gen
dweibull_gen
erlang_gen
expon_gen
exponpow_gen
exponweib_gen
f_gen
fatiguelife_gen
fisk_gen
foldcauchy_gen
foldnorm_gen
frechet_l_gen
frechet_r_gen
gamma_gen
gausshyper_gen
general_cont_ppf
genexpon_gen
genextreme_gen
gengamma_gen
genhalflogistic_gen
genlogistic_gen
genpareto_gen
geom_gen
gilbrat_gen
gompertz_gen
gumbel_l_gen
gumbel_r_gen
halfcauchy_gen
halflogistic_gen
halfnorm_gen
hypergeom_gen
hypsecant_gen
invgamma_gen
invnorm_gen
invweibull_gen
johnsonsb_gen
johnsonsu_gen
ksone_gen
kstwobign_gen
laplace_gen
levy_gen
levy_l_gen
levy_stable_gen
loggamma_gen
logistic_gen
loglaplace_gen
lognorm_gen
logser_gen
lomax_gen
maxwell_gen
mielke_gen
nakagami_gen
nbinom_gen
ncf_gen
nct_gen
ncx2_gen
norm_gen
pareto_gen
planck_gen
poisson_gen
powerlaw_gen
powerlognorm_gen
powernorm_gen
randint_gen
rayleigh_gen
rdist_gen
recipinvgauss_gen
reciprocal_gen
rice_gen
rv_continuous - A Generic continuous random variable
rv_discrete - A generic discrete random variable
rv_frozen
semicircular_gen
t_gen
triang_gen
truncexpon_gen
truncnorm_gen
tukeylambda_gen
uniform_gen
vonmises_gen
wald_gen
wrapcauchy_gen
zipf_gen

Function summary

argsreduce(cond, *args)
entropy(pk, qk = None)
make_dict(keys, values)
reverse_dict(dict)
valarray(shape, value = nan, typecode = None)

Functions

argsreduce(cond, *args)

Return a sequence of arguments converted to the dimensions of cond
entropy(pk, qk = None)

S = entropy(pk,qk=None)

calculate the entropy of a distribution given the p_k values S = -sum(pk * log(pk),axis=0)

If qk is not None, then compute a relative entropy S = -sum(pk * log(pk / qk),axis=0)

Routine will normalize pk and qk if they don't sum to 1
make_dict(keys, values)
reverse_dict(dict)
valarray(shape, value = nan, typecode = None)

Return an array of all value.

Imported Names