# Can you add binomial distributions?

## Can you add binomial distributions?

A Binomial distributed random variable X ~ B(n, p) can be considered as the sum of n Bernouli distributed random variables. So the sum of two Binomial distributed random variable X ~ B(n, p) and Y ~ B(m, p) is equivalent to the sum of n + m Bernouli distributed random variables, which means Z=X+Y ~ B(n+m, p).

What is negative binomial probability distribution?

In probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures (denoted r) occurs.

Are the negative binomial and geometric distributions related describe with examples?

It deals with the number of trials required for a single success. Thus, the geometric distribution is negative binomial distribution where the number of successes (r) is equal to 1. An example of a geometric distribution would be tossing a coin until it lands on heads.

### Is negative binomial sum of geometric?

A negative binomial distribution with r = 1 is a geometric distribution. Also, the sum of r independent Geometric(p) random variables is a negative binomial(r, p) random variable. If each Xi is distributed as negative binomial(ri,p) then ∑ Xi is distributed as negative binomial(∑ ri, p). Let Y ∼ binomial(n, p).

What is the difference between binomial distribution and negative binomial distribution?

Binomial distribution describes the number of successes k achieved in n trials, where probability of success is p. Negative binomial distribution describes the number of successes k until observing r failures (so any number of trials greater then r is possible), where probability of success is p.

What does negative binomial distribution mean?

The negative binomial distribution is a probability distribution that is used with discrete random variables. This type of distribution concerns the number of trials that must occur in order to have a predetermined number of successes.

#### What is negative binomial parameter?

As its name implies, the negative binomial shape parameter, k, describes the shape of a negative binomial distribution. In other words, k is only a reasonable measure to the extent that your data represent a negative binomial distribution.

What is a negative binomial regression model?

Negative binomial regression is implemented using maximum likelihood estimation. The traditional model and the rate model with offset are demonstrated, along with regression diagnostics. Negative binomial regression is a type of generalized linear model in which the dependent variable is a count of the number of times an event occurs.

What are some examples of binomial distribution?

Examples of binomial distribution problems: The number of defective/non-defective products in a production run. Yes/No Survey (such as asking 150 people if they watch ABC news). Vote counts for a candidate in an election. The number of successful sales calls. The number of male/female workers in a company