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 […]
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 […]
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 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 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 […]
Logarithmic Series Distribution A discrete random variable X is said to have logarithmic series distribution if its probability density function is defined as, where q is the parameter which lies between zero to one. The name is justified as the probabilities for the various values of x are the terms of the […]
Definition A discrete random variable X is said to have negative binomial distribution if its probability density function is defined as, where r>0 and 0<=p<=1 are the two parameter of the distribution such that p+q=1. f(x;r,p) is the probability of getting exactly r successes in (x+r) independent bernoulli trials. Properties of Negative Binomial Distribution […]
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 […]
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 […]
The Poisson distribution is the discrete probability distribution of the number of events occurring in a given time period, given the average number of times the event occurs over that time period. A discrete random variable X is said to have Poisson distribution if its probability function is defined as, where λ is the pararmeter of the distribution and […]
