Pearson system random numbers
r = pearsrnd(mu,sigma,skew,kurt,m,n)
r = pearsrnd(mu,sigma,skew,kurt)
r = pearsrnd(mu,sigma,skew,kurt,m,n,...)
r
= pearsrnd(mu,sigma,skew,kurt,[m,n,...])
[r,type] = pearsrnd(...)
[r,type,coefs] = pearsrnd(...)
r = pearsrnd(mu,sigma,skew,kurt,m,n)
returns
an m
byn
matrix of random numbers
drawn from the distribution in the Pearson system with mean mu
,
standard deviation sigma
, skewness skew
,
and kurtosis kurt
. The parameters mu
, sigma
, skew
,
and kurt
must be scalars.
Note:
Because

Some combinations of moments are not valid; in particular, the kurtosis must be greater than the square of the skewness plus 1. The kurtosis of the normal distribution is defined to be 3.
r = pearsrnd(mu,sigma,skew,kurt)
returns
a scalar value.
r = pearsrnd(mu,sigma,skew,kurt,m,n,...)
or r
= pearsrnd(mu,sigma,skew,kurt,[m,n,...])
returns an m
byn
by...
array.
[r,type] = pearsrnd(...)
returns the type
of the specified distribution within the Pearson system. type
is
a scalar integer from 0
to 7
.
Set m
and n
to 0
to
identify the distribution type without generating any random values.
The seven distribution types in the Pearson system correspond to the following distributions:
0
— Normal distribution
1
— Fourparameter beta distribution
2
— Symmetric fourparameter beta distribution
3
— Threeparameter gamma distribution
4
— Not related to any standard
distribution. The density is proportional to:
(1 + ((x – a)/b)^{2})^{–c} exp(–d arctan((x – a)/b)).
5
— Inverse gamma locationscale
distribution
6
— F locationscale distribution
7
— Student's t locationscale distribution
[r,type,coefs] = pearsrnd(...)
returns
the coefficients coefs
of the quadratic polynomial
that defines the distribution via the differential equation
$$\frac{d}{dx}\mathrm{log}(p(x))=\frac{(a+x)}{c(0)+c(1)x+c(2){x}^{2}}.$$
Generate random values from the standard normal distribution:
r = pearsrnd(0,1,0,3,100,1); % Equivalent to randn(100,1)
[r,type] = pearsrnd(0,1,1,4,0,0); r = [] type = 1
[1] Johnson, N.L., S. Kotz, and N. Balakrishnan (1994) Continuous Univariate Distributions, Volume 1, WileyInterscience, Pg 15, Eqn 12.33.