I have a discete probability distribution (histogram) and want to invoke rand to produce n random samples that follow the distribution specified by the histogram -how?

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kujoeb
kujoeb 2017-2-9
回答： Image Analyst 2017-2-10
I have a distribution specified by a 1d histogram, say [1 , 10; 2 , 50; 3 , 10; 4 , 30]
now I want to invoke rand to produce n discrete random samples (of value 1,2,3, or 4), such that the output distribution of the random samples matches closely the distribution specified by the histogram.
E.g. in this example for n=10 I would expect the output vector to have one 1, five 2s, one 3, and three 4s or a result that would be very close to it. How can I ensure that through rand()?

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回答（3 个）

Bjorn Gustavsson
Bjorn Gustavsson 2017-2-9
0, always start by looking for a solution at the file exchange. 1, I did a quick search and perhaps these submissions solves your problem:
arbrand
random-numbers-from-a-user-defined-piecewise-polynomial-distribution
obs-from-arbitrary-pdf
HTH
Roger Stafford
Roger Stafford 2017-2-9
编辑：Roger Stafford 2017-2-9
p = sum(bsxfun(@le,[0,0.1,0.6,0.7],rand(n,1)),2);
(Note: Since this is a probability distribution, you cannot always expect “ the output vector to have one 1, five 2s, one 3, and three 4s or a result that would be very close to it. ” There is always a finite probability that the result would be otherwise.)
Image Analyst
Image Analyst 2017-2-10
You need "inverse transform sampling" : https://en.wikipedia.org/wiki/Inverse_transform_sampling Basically compute the CDF of the distribution, and use it to get samples.
I attach an m-file where I get samples drawn from a Rayleigh distribution.
You might also look at RANDRAW which does these distributions: Alpha, Anglit, Antilognormal, Arcsin, Bernoulli, Bessel, Beta, Binomial, Bradford, Burr, Cauchy, Chi, Chi-Square (Non-Central), Chi-Square (Central), Cobb-Douglas, Cosine, Double-Exponential, Erlang, Exponential, Extreme-Value, F (Central), F (Non-Central), Fisher-Tippett, Fisk, Frechet, Furry, Gamma, Generalized Inverse Gaussian, Generalized Hyperbolic, Geometric, Gompertz, Gumbel, Half-Cosine, Hyperbolic Secant, Hypergeometric, Inverse Gaussian, Laplace, Logistic, Lognormal, Lomax, Lorentz, Maxwell, Nakagami, Negative Binomial, Normal, Normal-Inverse-Gaussian (NIG), Pareto, Pareto2, Pascal, Planck, Poisson, Quadratic, Rademacher, Rayleigh, Rice, Semicircle, Skellam, Student's-t, Triangular, Truncated Normal, Tukey-Lambda, U-shape, Uniform (continuous), Von Mises, Wald, Weibull, Wigner Semicircle, Yule, Zeta, Zipf

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AI, Data Science, and Statistics Statistics and Machine Learning Toolbox Probability Distributions Discrete Distributions Binomial Distribution
AI, Data Science, and Statistics Statistics and Machine Learning Toolbox Probability Distributions Discrete Distributions Hypergeometric Distribution
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