More Probability Distribution Functions

There are similar probability distribution functions for many other distributions. They will only be listed here as a reference as they work very similarly to the normal distribution functions as discussed previously.

The Binomial Distribution

• dbinom(x, size, prob)

This gives the density or probability of getting the value x in a binomial distribution with size = n (number of trials) and prob = p (probability of success).

• pbinom(q, size, prob, lower.tail = TRUE)

This gives the probability of getting a value of q or less in a binomial distribution with size = n (number of trials) and prob = p (probability of success).

• qbinom(p, size, prob, lower.tail = TRUE)

This gives the critical value of the p^th percentile (quantile) in a binomial distribution with size = n (number of trials) and prob = p (probability of success).

The Geometric Distribution

• dgeom(x, prob)

This gives the density or probability of getting the value x in a geometric distribution with prob = p (probability of success).

• pgeom(q, prob, lower.tail = TRUE)

This gives the probability of getting q or fewer failures in a geometric distribution with prob = p (probability of success).

• qgeom(p, prob, lower.tail = TRUE)

This gives the critical value of the p^th percentile (quantile) in a geometric distribution with prob = p (probability of success).

The Poisson Distribution

• dpois(x, lambda)

This gives the density or probability of getting the value x in a Poisson distribution with lambda = λ (parameter value).

• ppois(q, lambda, lower.tail = TRUE)

This gives the probability of getting a value of q or less in a Poisson distribution with lambda = λ (parameter value).

• qpois(p, lambda, lower.tail = TRUE)

This gives the critical value of the p^th percentile (quantile) in a Poisson distribution with lambda = λ (parameter value).

The t Distribution

• dt(x, df)

This gives the density or probability of getting the value x in a t distribution with df = df (degrees of freedom).
(This function is not used as often because the t distribution is a continuous distribution.)

• pt(q, df, lower.tail = TRUE)

This gives the probability of getting a value of q or less in a t distribution with df = df (degrees of freedom).

• qt(p, df, lower.tail = TRUE)

This gives the critical value of the p^th percentile (quantile) in a t distribution with df = df (degrees of freedom).

The Uniform Distribution

• dunif(x, min = 0, max = 1)

This gives the density or probability of getting the value x in a uniform distribution with min and max equal to the lower and upper limits of the distribution.
(This function is not used as often because the uniform distribution is a continuous distribution.)

• punif(q, min = 0, max = 1, lower.tail = TRUE)

This gives the probability of getting a value of q or less in a uniform distribution with min and max equal to the lower and upper limits of the distribution.

• qunif(p, min = 0, max = 1, lower.tail = TRUE)

This gives the critical value of the p^th percentile (quantile) in a uniform distribution with min and max equal to the lower and upper limits of the distribution.

The Exponential Distribution

• dexp(x, rate = 1)

This gives the density or probability of getting the value x in an exponential distribution with rate = λ (parameter value).
(This function is not used as often because the exponential distribution is a continuous distribution.)

• pexp(q, rate = 1, lower.tail = TRUE)

This gives the probability of getting a value of q or less in an exponential distribution with rate = λ (parameter value).

• qexp(p, rate = 1, lower.tail = TRUE)

This gives the critical value of the p^th percentile (quantile) in an exponential distribution with rate = λ (parameter value).

The χ² Distribution

• dchisq(x, df)

This gives the density or probability of getting the value x in a χ² distribution with df = df (degrees of freedom).
(This function is not used as often because the χ² distribution is a continuous distribution.)

• pchisq(q, df, lower.tail = TRUE)

This gives the probability of getting a value of q or less in a χ² distribution with df = df (degrees of freedom).

• qchisq(p, df, lower.tail = TRUE)

This gives the critical value of the p^th percentile (quantile) in a χ² distribution with df = df (degrees of freedom).

The F Distribution

• df(x, df1, df2)

This gives the density or probability of getting the value x in an F distribution with df1 and df2 equal to the numerator and denominator degrees of freedom.
(This function is not used as often because the F distribution is a continuous distribution.)

• pf(q, df1, df2, lower.tail = TRUE)

This gives the probability of getting a value of q or less in an F distribution with df1 and df2 equal to the numerator and denominator degrees of freedom.

• qf(p, df1, df2, lower.tail = TRUE)

This gives the critical value of the p^th percentile (quantile) in an F distribution with df1 and df2 equal to the numerator and denominator degrees of freedom.

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