| beta_cdf (x a, b) | Function File |
| 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). |
| beta_inv (x a, b) | Function File |
| For each component of x compute the quantile (the inverse of the CDF) at x of the Beta distribution with parameters a and b. |
| beta_pdf (x a, b) | Function File |
| For each element of x returns the PDF at x of the beta distribution with parameters a and b. |
| beta_rnd (a b, r, c) | Function File |
| beta_rnd (a b, sz) | Function File |
Return an r by c or size (sz) 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. |
| binomial_cdf (x n, p) | Function File |
| For each element of x compute the CDF at x of the binomial distribution with parameters n and p. |
| binomial_inv (x n, p) | Function File |
| For each element of x compute the quantile at x of the binomial distribution with parameters n and p. |
| binomial_pdf (x n, p) | Function File |
| For each element of x compute the probability density function (PDF) at x of the binomial distribution with parameters n and p. |
| binomial_rnd (n p, r, c) | Function File |
| binomial_rnd (n p, sz) | Function File |
Return an r by c or a size (sz) 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. |
| cauchy_cdf (x lambda, sigma) | Function File |
| 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. |
| cauchy_inv (x lambda, sigma) | Function File |
| 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. |
| cauchy_pdf (x lambda, sigma) | Function File |
| 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. |
| cauchy_rnd (lambda sigma, r, c) | Function File |
| cauchy_rnd (lambda sigma, sz) | Function File |
Return an r by c or a size (sz) 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. |
| chisquare_cdf (x n) | Function File |
| For each element of x compute the cumulative distribution function (CDF) at x of the chisquare distribution with n degrees of freedom. |
| chisquare_inv (x n) | Function File |
| For each element of x compute the quantile (the inverse of the CDF) at x of the chisquare distribution with n degrees of freedom. |
| chisquare_pdf (x n) | Function File |
| For each element of x compute the probability density function (PDF) at x of the chisquare distribution with k degrees of freedom. |
| chisquare_rnd (n r, c) | Function File |
| chisquare_rnd (n sz) | Function File |
Return an r by c or a size (sz) 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. |
| discrete_cdf (x v, p) | Function File |
| 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. |
| discrete_inv (x v, p) | Function File |
| 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. |
| discrete_pdf (x v, p) | Function File |
| 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. |
| discrete_rnd (n v, p) | Function File |
| discrete_rnd (v p, r, c) | Function File |
| discrete_rnd (v p, sz) | Function File |
|
Generate a row vector containing a random sample of size n from
the univariate distribution which assumes the values in v with
probabilities p. n must be a scalar.
If r and c are given create a matrix with r rows and c columns. Or if sz is a vector create a matrix of size sz. |
| empirical_cdf (x data) | Function File |
| For each element of x compute the cumulative distribution function (CDF) at x of the empirical distribution obtained from the univariate sample data. |
| empirical_inv (x data) | Function File |
| 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. |
| empirical_pdf (x data) | Function File |
| For each element of x compute the probability density function (PDF) at x of the empirical distribution obtained from the univariate sample data. |
| empirical_rnd (n data) | Function File |
| empirical_rnd (data r, c) | Function File |
| empirical_rnd (data sz) | Function File |
|
Generate a bootstrap sample of size n from the empirical
distribution obtained from the univariate sample data.
If r and c are given create a matrix with r rows and c columns. Or if sz is a vector create a matrix of size sz. |
| exponential_cdf (x lambda) | Function File |
|
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. |
| exponential_inv (x lambda) | Function File |
| For each element of x compute the quantile (the inverse of the CDF) at x of the exponential distribution with parameter lambda. |
| exponential_pdf (x lambda) | Function File |
| For each element of x compute the probability density function (PDF) of the exponential distribution with parameter lambda. |
| exponential_rnd (lambda r, c) | Function File |
| exponential_rnd (lambda sz) | Function File |
|
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. Or if sz is a vector
create a matrix of size sz.
If r and c are omitted the size of the result matrix is the size of lambda. |
| f_cdf (x m, n) | Function File |
| 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). |
| f_inv (x m, n) | Function File |
| For each component of x compute the quantile (the inverse of the CDF) at x of the F distribution with parameters m and n. |
| f_pdf (x m, n) | Function File |
| For each element of x compute the probability density function (PDF) at x of the F distribution with m and n degrees of freedom. |
| f_rnd (m n, r, c) | Function File |
| f_rnd (m n, sz) | Function File |
|
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 sz is a vector the random samples are in a matrix of
size sz.
If r and c are omitted the size of the result matrix is the common size of m and n. |
| gamma_cdf (x a, b) | Function File |
| For each element of x compute the cumulative distribution function (CDF) at x of the Gamma distribution with parameters a and b. |
| gamma_inv (x a, b) | Function File |
| For each component of x compute the quantile (the inverse of the CDF) at x of the Gamma distribution with parameters a and b. |
| gamma_pdf (x a, b) | Function File |
| For each element of x return the probability density function (PDF) at x of the Gamma distribution with parameters a and b. |
| gamma_rnd (a b, r, c) | Function File |
| gamma_rnd (a b, sz) | Function File |
Return an r by c or a size (sz) 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. |
| geometric_cdf (x p) | Function File |
| For each element of x compute the CDF at x of the geometric distribution with parameter p. |
| geometric_inv (x p) | Function File |
| For each element of x compute the quantile at x of the geometric distribution with parameter p. |
| geometric_pdf (x p) | Function File |
| For each element of x compute the probability density function (PDF) at x of the geometric distribution with parameter p. |
| geometric_rnd (p r, c) | Function File |
| geometric_rnd (p sz) | Function File |
|
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 given create a matrix with r rows and c columns. Or if sz is a vector create a matrix of size sz. |
| hypergeometric_cdf (x m, t, n) | Function File |
|
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. |
| hypergeometric_inv (x m, t, n) | Function File |
|
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. |
| hypergeometric_pdf (x m, t, n) | Function File |
|
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. |
| hypergeometric_rnd (n_size m, t, n) | Function File |
| hypergeometric_rnd (m t, n, r, c) | Function File |
| hypergeometric_rnd (m t, n, sz) | Function File |
|
Generate a row vector containing a random sample of size n_size
from the hypergeometric distribution with parameters m t,
and n.
If r and c are given create a matrix with r rows and c columns. Or if sz is a vector create a matrix of size sz. The parameters m t, and n must positive integers with m and n not greater than t. |
| kolmogorov_smirnov_cdf (x tol) | Function File |
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 = |
| laplace_cdf (x) | Function File |
| For each element of x compute the cumulative distribution function (CDF) at x of the Laplace distribution. |
| laplace_inv (x) | Function File |
| For each element of x compute the quantile (the inverse of the CDF) at x of the Laplace distribution. |
| laplace_pdf (x) | Function File |
| For each element of x compute the probability density function (PDF) at x of the Laplace distribution. |
| laplace_rnd (r c) | Function File |
| laplace_rnd (sz); | Function File |
| Return an r by c matrix of random numbers from the Laplace distribution. Or is sz is a vector create a matrix of sz. |
| logistic_cdf (x) | Function File |
| For each component of x compute the CDF at x of the logistic distribution. |
| logistic_inv (x) | Function File |
| For each component of x compute the quantile (the inverse of the CDF) at x of the logistic distribution. |
| logistic_pdf (x) | Function File |
| For each component of x compute the PDF at x of the logistic distribution. |
| logistic_rnd (r c) | Function File |
| logistic_rnd (sz) | Function File |
| Return an r by c matrix of random numbers from the logistic distribution. Or is sz is a vector create a matrix of sz. |
| lognormal_cdf (x a, v) | Function File |
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. |
| lognormal_inv (x a, v) | Function File |
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. |
| lognormal_pdf (x a, v) | Function File |
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. |
| lognormal_rnd (a v, r, c) | Function File |
| lognormal_rnd (a v, sz) | Function File |
|
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.
Or if sz is a vector create a matrix of size sz.
If r and c are omitted the size of the result matrix is the common size of a and v. |
| normal_cdf (x m, v) | Function File |
|
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. |
| normal_inv (x m, v) | Function File |
|
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. |
| normal_pdf (x m, v) | Function File |
|
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. |
| normal_rnd (m v, r, c) | Function File |
| normal_rnd (m v, sz) | Function File |
Return an r by c or size (sz) 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. |
| pascal_cdf (x n, p) | Function File |
|
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. |
| pascal_inv (x n, p) | Function File |
|
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. |
| pascal_pdf (x n, p) | Function File |
|
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. |
| pascal_rnd (n p, r, c) | Function File |
| pascal_rnd (n p, sz) | Function File |
|
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. Or if sz is a vector create a matrix of size sz. |
| poisson_cdf (x lambda) | Function File |
| For each element of x compute the cumulative distribution function (CDF) at x of the Poisson distribution with parameter lambda. |
| poisson_inv (x lambda) | Function File |
| For each component of x compute the quantile (the inverse of the CDF) at x of the Poisson distribution with parameter lambda. |
| poisson_pdf (x lambda) | Function File |
| For each element of x compute the probability density function (PDF) at x of the poisson distribution with parameter lambda. |
| poisson_rnd (lambda r, c) | Function File |
|
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. |
| stdnormal_cdf (x) | Function File |
| For each component of x compute the CDF of the standard normal distribution at x. |
| stdnormal_inv (x) | Function File |
| For each component of x compute compute the quantile (the inverse of the CDF) at x of the standard normal distribution. |
| stdnormal_pdf (x) | Function File |
| For each element of x compute the probability density function (PDF) of the standard normal distribution at x. |
| stdnormal_rnd (r c) | Function File |
| stdnormal_rnd (sz) | Function File |
Return an r by c or size (sz) matrix of
random numbers from the standard normal distribution.
|
| t_cdf (x n) | Function File |
| 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). |
| t_inv (x n) | Function File |
| For each component of x compute the quantile (the inverse of the CDF) at x of the t (Student) distribution with parameter n. |
| t_pdf (x n) | Function File |
| For each element of x compute the probability density function (PDF) at x of the t (Student) distribution with n degrees of freedom. |
| t_rnd (n r, c) | Function File |
| t_rnd (n sz) | Function File |
|
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. Or if sz is a
vector create a matrix of size sz.
If r and c are omitted the size of the result matrix is the size of n. |
| uniform_cdf (x a, b) | Function File |
|
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. |
| uniform_inv (x a, b) | Function File |
|
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. |
| uniform_pdf (x a, b) | Function File |
|
For each element of x compute the PDF at x of the uniform
distribution on [a b].
Default values are a = 0 b = 1. |
| uniform_rnd (a b, r, c) | Function File |
| uniform_rnd (a b, sz) | Function File |
Return an r by c or a size (sz) 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. |
| weibull_cdf (x alpha, sigma) | Function File |
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. |
| weibull_inv (x lambda, alpha) | Function File |
| Compute the quantile (the inverse of the CDF) at x of the Weibull distribution with shape parameter alpha and scale parameter sigma. |
| weibull_pdf (x alpha, sigma) | Function File |
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. |
| weibull_rnd (alpha sigma, r, c) | Function File |
| weibull_rnd (alpha sigma, sz) | Function File |
|
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. Or if sz
is a vector return a matrix of size sz.
If r and c are omitted the size of the result matrix is the common size of alpha and sigma. |
| wiener_rnd (t d, n) | Function File |
|
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. |