Probability Distributions in Statistics

In statistics, probability distributions are very important measure which related to the random variable and statistical data. Every data patern follows a probability distribution. Continuous data follow the continuous distribution and discrete data follow the discrete distributions. According to wikipedia, “In probability theory and statistics, a probability distribution is the mathematical function that gives the […]

Gamma Distribution definition, formula and applications

In probabilistic statistics, the gamma distribution is a two-parameter family of continuous probability distributions which is widely used in different sectors. The exponential distribution, Erlang distribution, and chi-square distribution are special cases of it. Gamma Distribution A continuous random variable X is said to have a generalised gamma distribution with parameter α and β if […]

Exponential Distribution definition, formula with applications

In probabilistic statistics, the exponential distribution is the probability distribution of the time between events in a Poisson point process where events occur continuously and independently at a constant average rate. It is a special case of the gamma distribution.   Definition A continuous random variable X is said to have an exponential distribution with […]

Uniform Distribution definition, formula and applications

Uniform Distribution There are various continuous probability distributions such as uniform distribution, normal distribution, exponential distribution, gamma distribution, beta distribution, weibul distribution, cauchy distribution ect. Uniform distribution is a univariate continuous probability distribution with two parameter a and b. A continuous random variable x is said to have a uniform distribution if the probability function is […]

Power Series Distribution definition, formula with applications

Power Series Distribution A discrete random variable X is said to have a generalised power series distribution if its probability function is given by,     where f(θ) is a generating function and  f(θ) is positive finite and diferentiable. Power series distribution is a discrete probability distribution. Properties of Power series distribution Some special properties […]

Geometric Distribution: Definition, Properties and Applications

  Definition   A discrete random variable X is said to have a geometric distribution if its probability density function is defined as,       where p is the only parameter of of geometric distribution which satisfy  0<=p<=1 and p+q=1.   Properties of Geometric Distribution Geometric distribution follows the lack memory property. The mean […]

Hypergeometric Distribution: Definition, Properties and Applications

In probability statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of k successes in n draws, without replacement, from a finite population of size N that contains exactly K objects with that feature, wherein each draw is either a success or a failure.   Mathetical definition A discrete random variable […]