Standard Distribution

A “standard” probability distribution refers to a specific type of probability distribution that has been standardized or normalized in a way that allows for easy comparison or analysis. For example, in the case of the normal distribution, a standard normal distribution has a mean (average) of 0 and a standard deviation of 1.

Standard distributions in R language basically five types like – Normal, Uniform ,Exponential,Binomial and Poisson.

Normal Distribution (Gaussian Distribution)

Normal Distribution is a continuous probability distribution that is symmetric and bell-shaped. It is characterized by its mean (μ) and standard deviation (σ). The standard normal distribution is a specific form of the normal distribution with μ = 0 and σ = 1.

Where:

• -∞ < x < ∞

Uniform Distribution

Uniform distribution is a probability distribution where all outcomes are equally likely. For example, rolling a fair six-sided die has a uniform distribution because each side has an equal chance of landing face up.

Where:

• a ≤ x ≤ b

Exponential Distribution

Exponential distribution is a continuous probability distribution that describes the time between events in a Poisson process. It is often used in situations involving the modeling of time intervals between events.

Where:

• x ≥ 0

Binomial Distribution

Binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials (experiments with two possible outcomes, typically success or failure).

Where:

• n: number of trials
• p: probability of success
• q: probability of failure (p=1-q)
• X: number of successes in n trials

Poisson Distribution

Poisson distribution is a discrete probability distribution that describes the number of events occurring in a fixed interval of time or space, given a constant average rate of occurrence.

Where:

• x = 0,1,2,3…

To get started, follow these necessary steps:-

Random number generation is a crucial aspect of statistical simulations and data analysis. R languauge is a powerful statistical computing language, generating random numbers from standard distributions is a routine task.