Transcription of Distributions: Uniform, Normal, Exponential
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Distributions: Uniform, Normal, Exponential
Distributions Recall that an integrable function f : R [0,1] such that Rf(x)dx = 1 is called a probability density function (pdf). The distribution function for the pdf is given by x F(x) = f(z)dz - . (corresponding to the cumulative distribution function for the discrete case). Sampling from the distribution corresponds to solving the equation rsample x= f(z)dz - . for rsample given random probability values 0 x 1. I. Uniform distribution probability density function (area under the curve = 1). p(x). 1. (b-a). a b x rsample 1. The pdf for values uniformly distributed across [a,b] is given by f(x) =.
When λ = 1, the distribution is called the standard exponential distribution.In this case, inverting the distribution is straight-forward; e.g., -nsample = loge(1-x) nsample = -loge(1-x) which is a closed form formula for obtaining a normalized sample value (nsample) using a random probability x.
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