- Function File: beta_cdf (X, A, B)
For each element of X, returns the CDF at X of the beta
distribution with parameters A and B, i.e., PROB (beta (A, B) <=
X).
- Function File: beta_inv (X, A, B)
For each component of X, compute the quantile (the inverse of the
CDF) at X of the Beta distribution with parameters A and B.
- Function File: beta_pdf (X, A, B)
For each element of X, returns the PDF at X of the beta
distribution with parameters A and B.
- Function File: beta_rnd (A, B, R, C)
Return an R by C matrix of random samples from the Beta
distribution with parameters A and B. Both A and B must be scalar
or of size R by C.
If R and C are omitted, the size of the result matrix is the
common size of A and B.
- Function File: binomial_cdf (X, N, P)
For each element of X, compute the CDF at X of the binomial
distribution with parameters N and P.
- Function File: binomial_inv (X, N, P)
For each element of X, compute the quantile at X of the binomial
distribution with parameters N and P.
- Function File: binomial_pdf (X, N, P)
For each element of X, compute the probability density function
(PDF) at X of the binomial distribution with parameters N and P.
- Function File: binomial_rnd (N, P, R, C)
Return an R by C matrix of random samples from the binomial
distribution with parameters N and P. Both N and P must be scalar
or of size R by C.
If R and C are omitted, the size of the result matrix is the
common size of N and P.
- Function File: cauchy_cdf (X, LAMBDA, SIGMA)
For each element of X, compute the cumulative distribution
function (CDF) at X of the Cauchy distribution with location
parameter LAMBDA and scale parameter SIGMA. Default values are
LAMBDA = 0, SIGMA = 1.
- Function File: cauchy_inv (X, LAMBDA, SIGMA)
For each element of X, compute the quantile (the inverse of the
CDF) at X of the Cauchy distribution with location parameter
LAMBDA and scale parameter SIGMA. Default values are LAMBDA = 0,
SIGMA = 1.
- Function File: cauchy_pdf (X, LAMBDA, SIGMA)
For each element of X, compute the probability density function
(PDF) at X of the Cauchy distribution with location parameter
LAMBDA and scale parameter SIGMA > 0. Default values are LAMBDA =
0, SIGMA = 1.
- Function File: cauchy_rnd (LAMBDA, SIGMA, R, C)
Return an R by C matrix of random samples from the Cauchy
distribution with parameters LAMBDA and SIGMA which must both be
scalar or of size R by C.
If R and C are omitted, the size of the result matrix is the
common size of LAMBDA and SIGMA.
- Function File: chisquare_cdf (X, N)
For each element of X, compute the cumulative distribution
function (CDF) at X of the chisquare distribution with N degrees
of freedom.
- Function File: chisquare_inv (X, N)
For each element of X, compute the quantile (the inverse of the
CDF) at X of the chisquare distribution with N degrees of freedom.
- Function File: chisquare_pdf (X, N)
For each element of X, compute the probability density function
(PDF) at X of the chisquare distribution with K degrees of freedom.
- Function File: chisquare_rnd (N, R, C)
Return an R by C matrix of random samples from the chisquare
distribution with N degrees of freedom. N must be a scalar or of
size R by C.
If R and C are omitted, the size of the result matrix is the size
of N.
- Function File: discrete_cdf (X, V, P)
For each element of X, compute the cumulative distribution
function (CDF) at X of a univariate discrete distribution which
assumes the values in v with probabilities P.
- Function File: discrete_inv (X, V, P)
For each component of X, compute the quantile (the inverse of the
CDF) at X of the univariate distribution which assumes the values
in V with probabilities P.
- Function File: discrete_pdf (X, V, P)
For each element of X, compute the probability density function
(pDF) at X of a univariate discrete distribution which assumes the
values in V with probabilities P.
- Function File: discrete_rnd (N, V, P)
Generate a row vector containing a random sample of size N from
the univariate distribution which assumes the values in V with
probabilities P.
Currently, N must be a scalar.
- Function File: empirical_cdf (X, DATA)
For each element of X, compute the cumulative distribution
function (CDF) at X of the empirical distribution obtained from
the univariate sample DATA.
- Function File: empirical_inv (X, DATA)
For each element of X, compute the quantile (the inverse of the
CDF) at X of the empirical distribution obtained from the
univariate sample DATA.
- Function File: empirical_pdf (X, DATA)
For each element of X, compute the probability density function
(PDF) at X of the empirical distribution obtained from the
univariate sample DATA.
- Function File: empirical_rnd (N, DATA)
Generate a bootstrap sample of size N from the empirical
distribution obtained from the univariate sample DATA.
- Function File: exponential_cdf (X, LAMBDA)
For each element of X, compute the cumulative distribution
function (CDF) at X of the exponential distribution with parameter
LAMBDA.
The arguments can be of common size or scalar.
- Function File: exponential_inv (X, LAMBDA)
For each element of X, compute the quantile (the inverse of the
CDF) at X of the exponential distribution with parameter LAMBDA.
- Function File: exponential_pdf (X, LAMBDA)
For each element of X, compute the probability density function
(PDF) of the exponential distribution with parameter LAMBDA.
- Function File: exponential_rnd (LAMBDA, R, C)
Return an R by C matrix of random samples from the exponential
distribution with parameter LAMBDA, which must be a scalar or of
size R by C.
If R and C are omitted, the size of the result matrix is the size
of LAMBDA.
- Function File: f_cdf (X, M, N)
For each element of X, compute the CDF at X of the F distribution
with M and N degrees of freedom, i.e., PROB (F (M, N) <= X).
- Function File: f_inv (X, M, N)
For each component of X, compute the quantile (the inverse of the
CDF) at X of the F distribution with parameters M and N.
- Function File: f_pdf (X, M, N)
For each element of X, compute the probability density function
(PDF) at X of the F distribution with M and N degrees of freedom.
- Function File: f_rnd (M, N, R, C)
Return an R by C matrix of random samples from the F distribution
with M and N degrees of freedom. Both M and N must be scalar or
of size R by C.
If R and C are omitted, the size of the result matrix is the
common size of M and N.
- Function File: gamma_cdf (X, A, B)
For each element of X, compute the cumulative distribution
function (CDF) at X of the Gamma distribution with parameters A
and B.
- Function File: gamma_inv (X, A, B)
For each component of X, compute the quantile (the inverse of the
CDF) at X of the Gamma distribution with parameters A and B.
- Function File: gamma_pdf (X, A, B)
For each element of X, return the probability density function
(PDF) at X of the Gamma distribution with parameters A and B.
- Function File: gamma_rnd (A, B, R, C)
Return an R by C matrix of random samples from the Gamma
distribution with parameters A and B. Both A and B must be scalar
or of size R by C.
If R and C are omitted, the size of the result matrix is the
common size of A and B.
- Function File: geometric_cdf (X, P)
For each element of X, compute the CDF at X of the geometric
distribution with parameter P.
- Function File: geometric_inv (X, P)
For each element of X, compute the quantile at X of the geometric
distribution with parameter P.
- Function File: geometric_pdf (X, P)
For each element of X, compute the probability density function
(PDF) at X of the geometric distribution with parameter P.
- Function File: geometric_rnd (P, R, C)
Return an R by C matrix of random samples from the geometric
distribution with parameter P, which must be a scalar or of size R
by C.
If R and C are omitted, the size of the result matrix is the size
of P.
- Function File: hypergeometric_cdf (X, M, T, N)
Compute the cumulative distribution function (CDF) at X of the
hypergeometric distribution with parameters M, T, and N. This is
the probability of obtaining not more than X marked items when
randomly drawing a sample of size N without replacement from a
population of total size T containing M marked items.
The parameters M, T, and N must positive integers with M and N not
greater than T.
- Function File: hypergeometric_inv (X, M, T, N)
For each element of X, compute the quantile at X of the
hypergeometric distribution with parameters M, T, and N.
The parameters M, T, and N must positive integers with M and N not
greater than T.
- Function File: hypergeometric_pdf (X, M, T, N)
Compute the probability density function (PDF) at X of the
hypergeometric distribution with parameters M, T, and N. This is
the probability of obtaining X marked items when randomly drawing
a sample of size N without replacement from a population of total
size T containing M marked items.
The arguments must be of common size or scalar.
- Function File: hypergeometric_rnd (N_SIZE, M, T, N)
Generate a row vector containing a random sample of size N_SIZE
from the hypergeometric distribution with parameters M, T, and N.
The parameters M, T, and N must positive integers with M and N not
greater than T.
- Function File: kolmogorov_smirnov_cdf (X, TOL)
Return the CDF at X of the Kolmogorov-Smirnov distribution,
Inf
Q(x) = SUM (-1)^k exp(-2 k^2 x^2)
k = -Inf
for X > 0.
The optional parameter TOL specifies the precision up to which the
series should be evaluated; the default is TOL = `eps'.
- Function File: laplace_cdf (X)
For each element of X, compute the cumulative distribution
function (CDF) at X of the Laplace distribution.
- Function File: laplace_inv (X)
For each element of X, compute the quantile (the inverse of the
CDF) at X of the Laplace distribution.
- Function File: laplace_pdf (X)
For each element of X, compute the probability density function
(PDF) at X of the Laplace distribution.
- Function File: laplace_rnd (R, C)
Return an R by C matrix of random numbers from the Laplace
distribution.
- Function File: logistic_cdf (X)
For each component of X, compute the CDF at X of the logistic
distribution.
- Function File: logistic_inv (X)
For each component of X, compute the quantile (the inverse of the
CDF) at X of the logistic distribution.
- Function File: logistic_pdf (X)
For each component of X, compute the PDF at X of the logistic
distribution.
- Function File: logistic_rnd (R, C)
Return an R by C matrix of random numbers from the logistic
distribution.
- Function File: lognormal_cdf (X, A, V)
For each element of X, compute the cumulative distribution
function (CDF) at X of the lognormal distribution with parameters
A and V. If a random variable follows this distribution, its
logarithm is normally distributed with mean `log (A)' and variance
V.
Default values are A = 1, V = 1.
- Function File: lognormal_inv (X, A, V)
For each element of X, compute the quantile (the inverse of the
CDF) at X of the lognormal distribution with parameters A and V.
If a random variable follows this distribution, its logarithm is
normally distributed with mean `log (A)' and variance V.
Default values are A = 1, V = 1.
- Function File: lognormal_pdf (X, A, V)
For each element of X, compute the probability density function
(PDF) at X of the lognormal distribution with parameters A and V.
If a random variable follows this distribution, its logarithm is
normally distributed with mean `log (A)' and variance V.
Default values are A = 1, V = 1.
- Function File: lognormal_rnd (A, V, R, C)
Return an R by C matrix of random samples from the lognormal
distribution with parameters A and V. Both A and V must be scalar
or of size R by C.
If R and C are omitted, the size of the result matrix is the
common size of A and V.
- Function File: normal_cdf (X, M, V)
For each element of X, compute the cumulative distribution
function (CDF) at X of the normal distribution with mean M and
variance V.
Default values are M = 0, V = 1.
- Function File: normal_inv (X, M, V)
For each element of X, compute the quantile (the inverse of the
CDF) at X of the normal distribution with mean M and variance V.
Default values are M = 0, V = 1.
- Function File: normal_pdf (X, M, V)
For each element of X, compute the probability density function
(PDF) at X of the normal distribution with mean M and variance V.
Default values are M = 0, V = 1.
- Function File: normal_rnd (M, V, R, C)
Return an R by C matrix of random samples from the normal
distribution with parameters M and V. Both M and V must be scalar
or of size R by C.
If R and C are omitted, the size of the result matrix is the
common size of M and V.
- Function File: pascal_cdf (X, N, P)
For each element of X, compute the CDF at x of the Pascal
(negative binomial) distribution with parameters N and P.
The number of failures in a Bernoulli experiment with success
probability P before the N-th success follows this distribution.
- Function File: pascal_inv (X, N, P)
For each element of X, compute the quantile at X of the Pascal
(negative binomial) distribution with parameters N and P.
The number of failures in a Bernoulli experiment with success
probability P before the N-th success follows this distribution.
- Function File: pascal_pdf (X, N, P)
For each element of X, compute the probability density function
(PDF) at X of the Pascal (negative binomial) distribution with
parameters N and P.
The number of failures in a Bernoulli experiment with success
probability P before the N-th success follows this distribution.
- Function File: pascal_rnd (N, P, R, C)
Return an R by C matrix of random samples from the Pascal
(negative binomial) distribution with parameters N and P. Both N
and P must be scalar or of size R by C.
If R and C are omitted, the size of the result matrix is the
common size of N and P.
- Function File: poisson_cdf (X, LAMBDA)
For each element of X, compute the cumulative distribution
function (CDF) at X of the Poisson distribution with parameter
lambda.
- Function File: poisson_inv (X, LAMBDA)
For each component of X, compute the quantile (the inverse of the
CDF) at X of the Poisson distribution with parameter LAMBDA.
- Function File: poisson_pdf (X, LAMBDA)
For each element of X, compute the probability density function
(PDF) at X of the poisson distribution with parameter LAMBDA.
- Function File: poisson_rnd (LAMBDA, R, C)
Return an R by C matrix of random samples from the Poisson
distribution with parameter LAMBDA, which must be a scalar or of
size R by C.
If R and C are omitted, the size of the result matrix is the size
of LAMBDA.
- Function File: stdnormal_cdf (X)
For each component of X, compute the CDF of the standard normal
distribution at X.
- Function File: stdnormal_inv (X)
For each component of X, compute compute the quantile (the inverse
of the CDF) at X of the standard normal distribution.
- Function File: stdnormal_pdf (X)
For each element of X, compute the probability density function
(PDF) of the standard normal distribution at X.
- Function File: stdnormal_rnd (R, C)
Return an R by C matrix of random numbers from the standard normal
distribution.
- Function File: t_cdf (X, N)
For each element of X, compute the CDF at X of the t (Student)
distribution with N degrees of freedom, i.e., PROB (t(N) <= X).
- Function File: t_inv (X, N)
For each component of X, compute the quantile (the inverse of the
CDF) at X of the t (Student) distribution with parameter N.
- Function File: t_pdf (X, N)
For each element of X, compute the probability density function
(PDF) at X of the T (Student) distribution with N degrees of
freedom.
- Function File: t_rnd (N, R, C)
Return an R by C matrix of random samples from the t (Student)
distribution with N degrees of freedom. N must be a scalar or of
size R by C.
If R and C are omitted, the size of the result matrix is the size
of N.
- Function File: uniform_cdf (X, A, B)
Return the CDF at X of the uniform distribution on [A, B], i.e.,
PROB (uniform (A, B) <= x).
Default values are A = 0, B = 1.
- Function File: uniform_inv (X, A, B)
For each element of X, compute the quantile (the inverse of the
CDF) at X of the uniform distribution on [A, B].
Default values are A = 0, B = 1.
- Function File: uniform_pdf (X, A, B)
For each element of X, compute the PDF at X of the uniform
distribution on [A, B].
Default values are A = 0, B = 1.
- Function File: uniform_rnd (A, B, R, C)
Return an R by C matrix of random samples from the uniform
distribution on [A, B]. Both A and B must be scalar or of size R
by C.
If R and C are omitted, the size of the result matrix is the
common size of A and B.
- Function File: weibull_cdf (X, ALPHA, SIGMA)
Compute the cumulative distribution function (CDF) at X of the
Weibull distribution with shape parameter ALPHA and scale
parameter SIGMA, which is
1 - exp(-(x/sigma)^alpha)
for X >= 0.
- Function File: weibull_inv (X, LAMBDA, ALPHA)
Compute the quantile (the inverse of the CDF) at X of the Weibull
distribution with shape parameter ALPHA and scale parameter SIGMA.
- Function File: weibull_pdf (X, ALPHA, SIGMA)
Compute the probability density function (PDF) at X of the Weibull
distribution with shape parameter ALPHA and scale parameter SIGMA
which is given by
alpha * sigma^(-alpha) * x^(alpha-1) * exp(-(x/sigma)^alpha)
for X > 0.
- Function File: weibull_rnd (ALPHA, SIGMA, R, C)
Return an R by C matrix of random samples from the Weibull
distribution with parameters ALPHA and SIGMA which must be scalar
or of size R by C.
If R and C are omitted, the size of the result matrix is the
common size of ALPHA and SIGMA.
- Function File: wiener_rnd (T, D, N)
Return a simulated realization of the D-dimensional Wiener Process
on the interval [0,T]. If D is omitted, D = 1 is used. The first
column of the return matrix contains time, the remaining columns
contain the Wiener process.
The optional parameter N gives the number of summands used for
simulating the process over an interval of length 1. If N is
omitted, N = 1000 is used.
&nbps