Expected Total Number of Runs

Computes the exact expected total run count for mutually independent Bernoulli trials whose success probabilities may vary by position.

Usage

runs_mean(prob)

Arguments

prob

A non-empty numeric vector. Its ith element is the success probability of the ith Bernoulli trial and must be finite and in the closed interval [0, 1].

Value

A scalar double giving the expected number of runs.

Details

The expectation is one plus the sum of the probabilities that successive observations differ. It is conditional on the supplied probabilities and the mutual-independence assumption.

Examples

runs_mean(c(0.15, 0.40, 0.75, 0.60))