Gamma Distribution

Gamma Distribution

Gamma Distribution Gamma distribution is used to model a continuous random variable which takes positive values. Gamma distribution is widely used in science and engineering to model a skewed distribution. In this tutorial, we are going to discuss various important statistical properties of gamma distribution like graph of gamma distribution for various parameter combination, derivation …

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Exponential Distribution | MGF | PDF | Mean | Variance

Exponential Distribution

The Exponential Distribution is one of the continuous distribution used to measure time the expected time for an event to occur. A continuous random variable $X$ is said to have an exponential distribution with parameter $\theta$ if its probability denisity function is given by $$ \begin{align*} f(x)&= \begin{cases} \theta e^{-\theta x}, & x>0;\theta>0 \\ 0, …

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Beta Type-II Distribution

Beta Type II Distribution

Beta Type-II distribution A continuous random variable $X$ is said to have a beta type-II distribution with parameters $m$ and $n$ if its p.d.f. is given by $$ \begin{align*} f(x)&= \begin{cases} \frac{1}{B(m,n)}\cdot\frac{x^{m-1}}{(1+x)^{m+n}}, & 0\leq x\leq\infty;m,n>0 \\ 0, & Otherwise. \end{cases} \end{align*} $$ where $B(m,n) =\frac{\Gamma m \Gamma n}{\Gamma (m+n)}$. In notation, it can be written …

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Beta Type-I Distribution Calculator with Examples

Beta Type I Distribution Calculator with Examples

Beta Type I Distribution Calculator Use this calculator to find the probability density and cumulative probabilities for Beta Type I distribution with parameter $\alpha$ and $\beta$. Beta Type I Distribution Calculator First Parameter $\alpha$: Second Parameter $\beta$ Value of x Calculate Results Probability density : f(x) Probability X less than x: P(X < x) Probability …

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Beta Type-I Distribution

Beta Type I Distribution

Beta Type-I Distribution A continuous random variable $X$ is said to have a beta type-I distribution with parameters $m$ and $n$ if its p.d.f. is given by $$ \begin{align*} f(x)&= \begin{cases} \frac{1}{B(m,n)}x^{m-1}(1-x)^{n-1}, & 0\leq x\leq 1;m,n>0 \\ 0, & Otherwise. \end{cases} \end{align*} $$ where $B(m,n) =\frac{\Gamma m \Gamma n}{\Gamma (m+n)}$. In notation, it can be …

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Continuous Uniform Distribution

Continuous Uniform Distribution

Continuous Uniform Distribution Continuous uniform distribution is the simplest of all the distributions in statistics. The density function of continuous uniform distribution is flat like a rectangle, hence it is often called rectangular distribution. The probability is uniformly distributed in a closed interval $[\alpha,\beta]$. A continuous random variable $X$ is said to have a continuous …

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Geometric Distribution

Geometric Distribution

Introduction Geometric distribution is used to model the situation where we are interested in finding the probability of number failures before first success or number of trials (attempts) to get first success in a repeated mutually independent Beronulli’s trials, each with probability of success $p$. There are two different definitions of geometric distributions one based …

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Poisson Distribution

Poisson Distribution

Poisson Distribution Poisson distribution helps to describe the probability of occurrence of a number of events in some given time interval or in a specified region. The time interval may be of any length, such as a minutes, a day, a week etc. Definition of Poisson Distribution A discrete random variable $X$ is said to …

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