Negative Binomial Distribution

Negative Binomial Dist

Negative Binomial Distribution A negative binomial distribution is based on an experiment which satisfies the following three conditions: An experiment consists of q sequence of independent Bernoulli’s trials (i.e., each trial can result in a success ($S$) or a failure ($F$)), The probability of success is constant from trial to trial, i.e., $P(S\text{ on trial …

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Geometric Distribution Calculator with Examples

Geometric Distribution Calculator

Geometric Distribution Calculator Geometric distribution calculator is used to find the probability and cumulative probabilities for geometric random variable given the probability of success ($p$). Geometric Distribution Calculator Probability of success (p): No. of failure before first success (x): Calculate Result Probability : P(X = x) Cumulative Probability : P(X ≤ x) Cumulative Probability : …

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Cauchy Distribution

Cauchy Distribution

Cauchy Distribution A continuous random variable $X$ is said to follow Cauchy distribution with parameters $\mu$ and $\lambda$ if its probability density function is given by $$ \begin{eqnarray}\label{eqch1} f(x; \mu, \lambda) &=& \begin{cases} \frac{\lambda}{\pi}\cdot \frac{1}{\lambda^2+(x-\mu)^2}, & -\infty < x < \infty; \\ & -\infty < \mu < \infty, \lambda>0; \\ 0, & Otherwise. \end{cases} \end{eqnarray} …

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Weibull Distribution Examples | Calculator | Two Parameter

Weibull Distribution Calculator with Examples

Weibull Distribution Calculator Use this calculator to find the probability density and cumulative probabilities for two parameter Weibull distribution with parameter $\alpha$ and $\beta$. Weibull Distribution Calculator Location parameter $\alpha$: Scale parameter $\beta$ Value of x Calculate Results Probability density : f(x) Probability X less than x: P(X < x) Probability X greater than x: …

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Weibull Distribution | Standard | Two Parameter | Mean | Mode

Weibull Distribution

Weibull Distribution Weibull distribution is one of the most widely used probability distribution in reliability engineering. Definition of Weibull Distribution A continuous random variable $X$ is said to have a Weibull distribution with three parameters $\mu$, $\alpha$ and $\beta$ if the random variable $Y =\big(\frac{X-\mu}{\beta}\big)^\alpha$ has the exponential distribution with p.d.f. $$ \begin{equation*} f(y) = …

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Laplace Distribution Calculator with Examples

Laplace Distribution Calculator

Laplace Distribution Calculator Use this calculator to find the probability density and cumulative probabilities for Laplace distribution with parameter $\mu$ and $\lambda$. Laplace Distribution Calculator Location parameter $\mu$: Scale parameter $\lambda$ Value of x Calculate Results Probability density : f(x) Probability X less than x: P(X < x) Probability X greater than x: P(X > …

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Laplace Distribution

Laplace Distribution

Laplace Distribution A continuous random variable $X$ is said to have a Laplace distribution (Double exponential distribution or bilateral exponential distribution), if its p.d.f. is given by $$ \begin{align*} f(x;\mu, \lambda)&= \begin{cases} \frac{\lambda}{2}e^{-\lambda|x-\mu|}, & -\infty < x< \infty; \\ & -\infty < \mu < \infty, \lambda >0; \\ 0, & Otherwise. \end{cases} \end{align*} $$ In …

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Log Normal Distribution Calculator With Examples

Log-Normal Distribution Calculator

Log-normal distribution calculator Log-normal Distribution Calculator is used to find mean, variance and probabilities of various type of events for Log-normal distribution with parameter $\mu$ and $\sigma^2$. Log-Normal Probability Calculator First Parameter ($\mu$) Second parameter ($\sigma$) P(X< A) P(X > B) P(A< X &lt B) and Outside A and B and Calculate Results Mean : …

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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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