API Documentation Generated by Endo, 2006-08-14
API Documentation Generated by Endo, 2006-08-14
all = alltrue
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_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_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 = asarray
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_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_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_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_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_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_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_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_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_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_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_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_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_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 = numpy.finfo(float).eps.item()
erlang = erlang_gen(a = 0.0, name = 'erlang', longname = 'An Erlang', shapes = 'n', extradoc = """ Erlang distribution (Gamma with integer shape parameter) """)
errp = special.errprint
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_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_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_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_gen(a = 0.0, name = 'fink', longname = 'A funk', shapes = 'c', extradoc = """ Fink distribution. Burr distribution with d=1. """)
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_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_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_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 = special.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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_gen(name = 'hypsecant', longname = 'A hyperbolic secant', extradoc = """ Hyperbolic secant distribution hypsecant.pdf(x) = 1/pi * sech(x) """)
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_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_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_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_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_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_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_gen(name = 'laplace', longname = 'A Laplace', extradoc = """ Laplacian distribution laplace.pdf(x) = 1/2*exp(-abs(x)) """)
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_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_gen(name = 'levy_stable', longname = 'A Levy-stable', shapes = 'alpha, beta', extradoc = """ Levy-stable distribution (only random variates available -- ignore other docs) """)
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_gen(name = 'logistic', longname = 'A logistic', extradoc = """ Logistic distribution logistic.pdf(x) = exp(-x)/(1+exp(-x))**2 """)
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_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_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_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_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_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_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_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_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_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_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_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_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 = mtrand.permutation
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_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_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_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_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 = mtrand.rand
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 = mtrand.random_sample
random_integers = mtrand.random_integers
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_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_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_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_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_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 = 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_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_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_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_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_gen(a = 0.0, b = 1.0, name = 'uniform', longname = 'A uniform', extradoc = """ Uniform distribution constant between loc and loc+scale """)
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_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 = 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 = 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_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_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 """)
Return a sequence of arguments converted to the dimensions of cond
S = entropy(pk,qk=None)
calculate the entropy of a distribution given the p_k values S = -sum(pk * log(pk))
If qk is not None, then compute a relative entropy S = -sum(pk * log(pk / qk))
Routine will normalize pk and qk if they don't sum to 1
Return an array of all value.
| Local name | Refers to |
|---|---|
| alltrue | numpy.alltrue |
| angle | numpy.angle |
| any | numpy.any |
| arange | numpy.arange |
| arcsin | numpy.arcsin |
| arctan | numpy.arctan |
| arctanh | numpy.arctanh |
| argmax | numpy.argmax |
| argsort | numpy.argsort |
| asarray | numpy.asarray |
| atleast_1d | numpy.atleast_1d |
| ceil | numpy.ceil |
| cos | numpy.cos |
| cosh | numpy.cosh |
| exp | numpy.exp |
| extract | numpy.extract |
| floor | numpy.floor |
| inf | numpy.inf |
| insert | numpy.insert |
| inspect | inspect |
| isinf | numpy.isinf |
| isnan | numpy.isnan |
| log | numpy.log |
| logical_and | numpy.logical_and |
| mtrand | numpy.random |
| nan | numpy.nan |
| ndarray | numpy.ndarray |
| nested_scopes | __future__.nested_scopes |
| new | new |
| newaxis | numpy.newaxis |
| nonzero | numpy.nonzero |
| numpy | numpy |
| ones | numpy.ones |
| optimize | scipy.optimize |
| pi | numpy.pi |
| polyval | numpy.polyval |
| product | numpy.product |
| put | numpy.put |
| putmask | numpy.putmask |
| ravel | numpy.ravel |
| repeat | numpy.repeat |
| reshape | numpy.reshape |
| r_ | numpy.r_ |
| scipy | scipy |
| shape | numpy.shape |
| sin | numpy.sin |
| sinh | numpy.sinh |
| special | scipy.special |
| sqrt | numpy.sqrt |
| st | scipy.stats.stats |
| sum | numpy.sum |
| take | numpy.take |
| tan | numpy.tan |
| tanh | numpy.tanh |
| types | types |
| vectorize | numpy.vectorize |
| where | numpy.where |
| zeros | numpy.zeros |