Continuous Uniform Distribution Calculator With Examples The continuous uniform distribution is the simplest probability distribution where all the values belonging to its support have the same probability density. It is also known as rectangular distribution. This tutorial will help you understand how to solve the numerical examples based on continuous uniform distribution. Continuous Uniform Distribution …
Normal Distribution Normal distribution is one of the most fundamental distribution in Statistics. It is also known as Gaussian distribution. Definition of Normal Distribution A continuous random variable $X$ is said to have a normal distribution with parameters $\mu$ and $\sigma^2$ if its probability density function is given by $$ \begin{equation*} f(x;\mu, \sigma^2) = \left\{ …
Log-normal Distribution The continuous random variable $X$ has a log-normal distribution if the random variable $Y=\ln (X)$ has a normal distribution with mean $\mu$ and standard deviation $\sigma$. The probability density function of $X$ is $$ \begin{aligned} f(x) & = \frac{1}{\sqrt{2\pi}\sigma x}e^{-\frac{1}{2\sigma^2}(\ln x -\mu)^2},x\geq 0 \end{aligned} $$ In Log-normal distribution $\mu$ is called location parameter, …
Cauchy Distribution Calculator Use this calculator to find the probability density and cumulative probabilities for Cauchy distribution with parameter $a$ and $b$. Cauchy Distribution Calculator Location parameter $\mu$: Scale parameter $\lambda$ Value of x Calculate Results Probability density : f(x) Probability X less than x: P(X < x) Probability X greater than x: P(X > …
Cauchy Distribution A continuous random variable $X$ is said to follow Cauchy distribution with parameters $\mu$ and $\lambda$ if its probability density function is given by $$ \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} …
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. $$ \begin{equation*} f(y) = …
Laplace Distribution Calculator Use this calculator to find the probability density and cumulative probabilities for Laplace distribution with parameter $\mu$ and $\lambda$. Laplace Distribution Calculator Location parameter $\mu$: Scale parameter $\lambda$ Value of x Calculate Results Probability density : f(x) Probability X less than x: P(X < x) Probability X greater than x: P(X > …
Laplace Distribution A continuous random variable $X$ is said to have a Laplace distribution (Double exponential distribution or bilateral exponential distribution), if its p.d.f. is given by $$ \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*} $$ In …
Gamma Distribution Gamma distribution is used to model a continuous random variable which takes positive values. Gamma distribution is widely used in science and engineering to model a skewed distribution. In this tutorial, we are going to discuss various important statistical properties of gamma distribution like graph of gamma distribution for various parameter combination, derivation …
The Exponential Distribution is one of the continuous distribution used to measure time the expected time for an event to occur. A continuous random variable $X$ is said to have an exponential distribution with parameter $\theta$ if its probability denisity function is given by $$ \begin{align*} f(x)&= \begin{cases} \theta e^{-\theta x}, & x>0;\theta>0 \\ 0, …
