Gamma Distribution Equation Formula Latex Code and Summary

Gamma Distribution

Tags: #Math #Statistics

Equation

$$\Gamma \left( a \right) = \int\limits_0^\infty {s^{a - 1} } e^{ - s} ds \\ P(x) = \frac{x^{\alpha-1} e^{-frac{x}{\theta}}}{\Gamma(\alpha) \theta^{\alpha}} \\ \mu = \alpha \theta \\ \sigma^{2} = \alpha \theta^{2} \\ \gamma_{1} = \frac{2}{\sqrt{\alpha}} \\ \gamma_{2} = \frac{6}{\alpha}$$

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}

Have Fun

Let's Vote for the Most Difficult Equation!

Introduction

$\Gamma \left( a \right) = \int\limits_0^\infty {s^{a - 1} } e^{ - s} ds \\ P(x) = \frac{x^{\alpha-1} e^{-frac{x}{\theta}}}{\Gamma(\alpha) \theta^{\alpha}} \\ \mu = \alpha \theta \\ \sigma^{2} = \alpha \theta^{2} \\ \gamma_{1} = \frac{2}{\sqrt{\alpha}} \\ \gamma_{2} = \frac{6}{\alpha}$

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}

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:

$\Gamma(a)$ : Gamma function of a
$\alpha$ : Gamma function parameter
$P(x) = \frac{x^{\alpha-1} e^{-frac{x}{\theta}}}{\Gamma(\alpha) \theta^{\alpha}}$ : PDF of gamma distributed random variable X.
$\mu = \alpha \theta$ : Mean of Gamma Distribution
$\sigma^{2} = \alpha \theta^{2}$ : Variance of Gamma Distribution
$\gamma_{1} = \frac{2}{\sqrt{\alpha}}$ : Skewness of Gamma Distribution
$\gamma_{2} = \frac{6}{\alpha}$ : Kurtosis of Gamma Distribution

Discussion

Comment to Make Wishes Come True

Leave your wishes (e.g. Passing Exams) in the comments and earn as many upvotes as possible to make your wishes come true

Kathryn Olson

My optimism is high for passing this exam.

2023-10-08 00:00
Reply

Olivia Evans reply to Kathryn Olson

Best Wishes.

2023-10-23 00:00:00.0
Reply
Anna King

I'm trying my best to ensure I pass this exam.

2023-04-29 00:00
Reply

Stephanie Robinson reply to Anna King

You can make it...

2023-04-30 00:00:00.0
Reply
Hugo Chandler

Hoping to get over the hurdle of this exam.

2023-01-04 00:00
Reply

Judy Bell reply to Hugo Chandler

Gooood Luck, Man!

2023-02-03 00:00:00.0
Reply