## 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