# Questions tagged [gamma-distribution]

For problems that are related to gamma-family probability distributions.

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### Average response/waiting time for aggregated tasks with Poisson arrival

Suppose there is a specific computation task with Poisson arrival rate $\lambda$ that could be aggregated in a way that when a task arrives and triggers a computation which lasts for $D$ seconds, if ...
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### Sufficiency in the exponential distribution

I am trying to show that given a random sample $\{X_i\}_{i=1}^n$ where $X_i\sim exp(\lambda^{-1})$, the statistic $T(\mathbf{X})=\sum_{i=1}^n X_i$ is sufficient by using only the definition. I have ...
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### Evaluating product of Upper Incomplete Gamma functions

I have checked several posts but couldn't find the equivalent of $\Gamma(m,a) \cdot \Gamma(m,b)$, where '$\cdot$' means multiplication. I suspect that it can be solved by applying the equivalent of ...
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### Sum of logarithmized Dirichlet R.V.

If $$\vec x \sim \mbox{dirichlet}(\alpha \mathbf1_k ),$$ what is the distribution (or approximation of): $$\sum_{i=1}^k \log(x_i)$$. I was able to find the solution using the characteristic ...
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### PDF of Ratio of Normal and Gamma Random Variables

Let $X \sim N(0,1)$ and $Y \sim \Gamma\left(\frac{k}{2}, \frac{1}{2}\right)$. If $X$ and $Y$ are independent, find the pdf of $$V=\frac{X}{\sqrt{Y/k}}.$$ For this problem, I introduced $U=X$, and ...
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### Modified Mean of Gamma Distribution

Let $X,Y$ be independent random variables such that $X \sim \operatorname{Gamma}(a,b)$ and $Y\sim \operatorname{Gamma}(c,b)$. We denote $M = E_{X,Y}\left[\frac{X}{X+Y}\right]$. We know that in the ...
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### kurtosis of a time series -

There is an excellent paper by David Warren, published in 1986 in the Journal of Hydrology, "Outflow Skewness in non-seasonal linear reservoirs with gamma-distributed inflows" (Volume 85, pp127-137; ...
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### Continuous random variable Poisson distribution

A computer manufacturer produces two types of laptops, Machine A and Machine B. They offer an automatic manufacturer's warranty of 3 years when a consumer buys one of their laptops, good for two free ...
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### (1st Post) Estimating the transformation of a gamma random variable with a lognormal distribution

If X is gamma(n,$\lambda$) distributed, what should $\alpha$ and $\beta$ be such that the constructed random variable $\beta*exp(\alpha X)$ is approximated by the lognormal(0,1) distribution when n is ...
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### Bootstrap estimation of the 95% confidence intervals for the 95% quantile for gamma distribution

I cant find any where information or algorithm how to apply in steps the bootstrap procedure to estimate the 95% confidence intervals for the 95% quantile from a random sample. Does anyone knows how ...
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### Confidence interval of Inverse Gamma distribution

Let's say I have a set of value that is inverse gamma distributed, how do I compute the 95% confidence interval? Is there a formula so that I can apply to find the range of interval?
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### distribution of sum of double exponential random variables

I want to find out whether there is a concise expression (i.e. not a convolution) for the distribution of a random variable A which is the sum of $n$ i.i.d. rv's $B_i$, which are themselves double ...
Has the continuous distribution with the following probability density function in $(0,1)$ a name? $f(x;\alpha,\beta)=\frac{1}{\alpha^\beta\Gamma(\beta)}(-\log x)^{\beta-1}x^{\frac{1-\alpha}{\alpha}}$...