pearsrnd
statistics: r = pearsrnd (mu, sigma, skew, kurt)
statistics: r = pearsrnd (mu, sigma, skew, kurt, m)
statistics: r = pearsrnd (mu, sigma, skew, kurt, m, n, …)
statistics: r = pearsrnd (mu, sigma, skew, kurt, [m, n, …])
statistics: [r, type, coefs] = pearsrnd (…)
Random arrays from the Pearson system of distributions.
r = pearsrnd (mu, sigma, skew, kurt)
returns a random value drawn from the distribution in the Pearson system with
mean mu, standard deviation sigma, skewness skew, and
kurtosis kurt. kurt is the (non-excess) kurtosis, and the
moments must satisfy kurt > skew^2 + 1.
pearsrnd (mu, sigma, skew, kurt, m,
n, …) or pearsrnd (…, [m, n, …])
returns an m-by-n-by-… array of random values, following
the size conventions of randn.
[r, type, coefs] = pearsrnd (…) also returns
the type of the Pearson distribution (an integer 0 to 7) in
type, and the three coefficients coefs =
[c0, c1, c2] of the denominator quadratic of the
Pearson differential equation for the standardized distribution, so that
f'(x) / f (x) = -(x + c1) /
(c0 + c1 x + c2 x^2).
The Pearson types are: 0 normal, 1 four-parameter beta,
2 symmetric four-parameter beta, 3 gamma, 4 (not a named
distribution), 5 inverse gamma, 6 beta prime, and 7
Student’s t. Type 4 is generated by numerical inversion of its
cumulative distribution function.
See also: johnsrnd, random, randn
Source Code: pearsrnd
Identify the Pearson type matching a set of moments
[r, type, coefs] = pearsrnd (0, 1, 0.75, 4)
r = 0.2812 type = 6 coefs = 0.938525 0.344262 0.020492
Draw a sample with a target mean, sd, skewness, and kurtosis
r = pearsrnd (10, 2, 1, 5, 1, 1000); [mean(r), std(r)]
ans = 10.0632 2.0653