Exploratory Data Analysis
1.3. EDA Techniques
1.3.6. Probability Distributions
22.214.171.124. Gallery of Distributions
|Probability Mass Function||
The binomial distribution is used when there are exactly two mutually
exclusive outcomes of a trial. These outcomes are appropriately
labeled "success" and "failure". The binomial distribution is used to
obtain the probability of observing x successes in N
trials, with the probability of success on a single trial denoted by
p. The binomial distribution assumes that p is fixed
for all trials.
The formula for the binomial probability mass function is
The following is the plot of the binomial probability density function for four values of p and n = 100.
|Cumulative Distribution Function||
The formula for the binomial cumulative probability function is
The following is the plot of the binomial cumulative distribution function with the same values of p as the pdf plots above.
|Percent Point Function||
The binomial percent point function does not exist in simple
closed form. It is computed numerically. Note that because
this is a discrete distribution that is only defined for integer
values of x, the percent point function is not smooth in the
way the percent point function typically is for a continuous
The following is the plot of the binomial percent point function with the same values of p as the pdf plots above.
|Comments||The binomial distribution is probably the most commonly used discrete distribution.|
The maximum likelihood estimator of p (n is fixed) is
|Software||Most general purpose statistical software programs support at least some of the probability functions for the binomial distribution.|