User:IssaRice/Gamma distribution: Difference between revisions

Latest revision as of 06:20, 5 February 2020

https://www.youtube.com/watch?v=Qjeswpm0cWY

ok, so given a poisson process, instead of asking the time until the next occurrence, we can ask for the total time taken until n things happen, and this will be the sum $T_{n} = \sum_{j = 1}^{n} X_{j}$ , where each $X_{j} \sim E x p o n e n t i a l (λ)$ . Now this sum happens to have distribution $G a m m a (n, λ)$ . This still doesn't explain what it means when $n$ (or $α$ as this parameter is usually called) is not a positive integer.

Revision as of 03:35, 5 February 2020 (view source) IssaRice (talk \| contribs) (Created page with "https://www.youtube.com/watch?v=Qjeswpm0cWY ok, so given a poisson process, instead of asking the time until the next occurrence, we can ask for the total time taken until n...")		Latest revision as of 06:20, 5 February 2020 (view source) IssaRice (talk \| contribs) No edit summary
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	https://www.youtube.com/watch?v=Qjeswpm0cWY		https://www.youtube.com/watch?v=Qjeswpm0cWY

	ok, so given a poisson process, instead of asking the time until the next occurrence, we can ask for the total time taken until n things happen, and this will be the sum <math>T_n = \sum_{j=1}^n X_j</math>, where each <math>X_j \sim \mathrm{Exponential}(\lambda)</math>. Now this sum happens to have distribution <math>\mathrm{Gamma}(n, \lambda)</math>.		ok, so given a poisson process, instead of asking the time until the next occurrence, we can ask for the total time taken until n things happen, and this will be the sum <math>T_n = \sum_{j=1}^n X_j</math>, where each <math>X_j \sim \mathrm{Exponential}(\lambda)</math>. Now this sum happens to have distribution <math>\mathrm{Gamma}(n, \lambda)</math>. This still doesn't explain what it means when <math>n</math> (or <math>\alpha</math> as this parameter is usually called) is not a positive integer.