CODEWITHSUNDEEP
statisticsdistribution
Math
Math

Reputation: 1294

Gumbel distribution

I have a silly question: If X has a Gumbel distribution with parameters mu (location) and beta>0 (scale) Then what would be the distribution of A.X, where A is constant.

thank you all.

Upvotes: 1

Views: 298

Answers (1)

rozsasarpi
rozsasarpi

Reputation: 1641

Probably your question is better suited for Cross Validated and a google search would give you the answer. That being said, if X is Gumbel distributed than a*X would be Gumbel distributed as well (a is constant, lower case is used to avoid ambiguity). Using that E[a*X] = a*E[X] and Var[a*X] = a^2*Var[X], where E[] and Var[] are the mean and variance, respectively. Then using the formulas which express the connection between mean, variance and distribution parameters (mu, beta), e.g. from here, one can show that a*X has the following parameters (denoted by underscore):

mu_ = A*mu and beta_ = A*beta

a*X ~ Gum(mi_, beta_)

Upvotes: 2

Related Questions