Gamma Distribution
Tags: #Math #StatisticsEquation
$$\Gamma \left( a \right) = \int\limits_0^\infty {s^{a - 1} } e^{ - s} ds \\ P(x) = \frac{x^{\alpha-1} e^{-frac{x}{\theta}}}{\Gamma(\alpha) \theta^{\alpha}} \\ \mu = \alpha \theta \\ \sigma^{2} = \alpha \theta^{2} \\ \gamma_{1} = \frac{2}{\sqrt{\alpha}} \\ \gamma_{2} = \frac{6}{\alpha}$$Latex Code
\Gamma \left( a \right) = \int\limits_0^\infty {s^{a - 1} } e^{ - s} ds \\
P(x) = \frac{x^{\alpha-1} e^{-frac{x}{\theta}}}{\Gamma(\alpha) \theta^{\alpha}} \\
\mu = \alpha \theta \\
\sigma^{2} = \alpha \theta^{2} \\
\gamma_{1} = \frac{2}{\sqrt{\alpha}} \\
\gamma_{2} = \frac{6}{\alpha}
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Introduction
Equation
Latex Code
\Gamma \left( a \right) = \int\limits_0^\infty {s^{a - 1} } e^{ - s} ds \\
P(x) = \frac{x^{\alpha-1} e^{-frac{x}{\theta}}}{\Gamma(\alpha) \theta^{\alpha}} \\
\mu = \alpha \theta \\
\sigma^{2} = \alpha \theta^{2} \\
\gamma_{1} = \frac{2}{\sqrt{\alpha}} \\
\gamma_{2} = \frac{6}{\alpha}
Explanation
Latex code for Gamma Distribution. A gamma distribution is a general type of statistical distribution that is related to the beta distribution and arises naturally in processes for which the waiting times between Poisson distributed events are relevant. Gamma distributions have two free parameters, labeled alpha and theta. We now let W denote the waiting time until the a-th event occurs and find the distribution of W. We could represent the situation as follows:
: Gamma function of a
: Gamma function parameter
: PDF of gamma distributed random variable X.
: Mean of Gamma Distribution
: Variance of Gamma Distribution
: Skewness of Gamma Distribution
: Kurtosis of Gamma Distribution
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