Power Series Distribution Let $T$ be any countable set of real numbers with no finite limit point and let $a(\cdot)$ be any real valued function defined on $T$. Then there exists a function $f(\theta)$ for all $\theta \in \Omega$ and $0<\theta<\infty$ such that it satisfies the power series expansion. Then the random variable $X$ with …
Negative Binomial Distribution Calculator This calculator is used to find the probability and cumulative probabilities for negative binomial random variable given the number of successes ($r$) and probability of success ($p$). Negative Binomial Distribution Calculator Number of successes (r): Probability of success (p): Number of failures (x): Calculate Result Probability : P(X = x) Cumulative …
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., $P(S\text{ on trial …
Geometric Distribution Calculator Geometric distribution calculator is used to find the probability and cumulative probabilities for geometric random variable given the probability of success ($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 : …
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 $$ \begin{eqnarray}\label{eqch1} f(x; \mu, \lambda) &=& \begin{cases} \frac{\lambda}{\pi}\cdot \frac{1}{\lambda^2+(x-\mu)^2}, & -\infty < x < \infty; \\ & -\infty < \mu < \infty, \lambda>0; \\ 0, & Otherwise. \end{cases} \end{eqnarray} …
Weibull Distribution Calculator Use this calculator to find the probability density and cumulative probabilities for two parameter Weibull distribution with parameter $\alpha$ and $\beta$. Weibull Distribution Calculator Location parameter $\alpha$: Scale parameter $\beta$ Value of x Calculate Results Probability density : f(x) Probability X less than x: P(X < x) Probability X greater than x: …
Weibull Distribution Weibull distribution is one of the most widely used probability distribution in reliability engineering. Definition of Weibull Distribution A continuous random variable $X$ is said to have a Weibull distribution with three parameters $\mu$, $\alpha$ and $\beta$ if the random variable $Y =\big(\frac{X-\mu}{\beta}\big)^\alpha$ has the exponential distribution with p.d.f. $$ \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 …
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 < B) and Outside A and B and Calculate Results Mean : …
