Exact One-Sided Tail Probability for the Run Count

Computes the inclusive lower or upper tail probability of the observed run count under mutually independent Bernoulli trials with fixed, supplied success probabilities.

Usage

runs_tail(x, prob, tail = c("lower", "upper"))

Arguments

x

A non-empty logical or numeric vector containing only zeroes and ones. It is the observed binary sequence.

prob

A numeric vector of the same length as x. Its ith element is the success probability of the ith trial and must lie in [0, 1].

tail

A character string selecting the inclusive "lower" tail, \(P(R \le r_{obs})\), or inclusive "upper" tail, \(P(R \ge r_{obs})\). Partial matching follows match.arg().

Value

An object of class runs_exact_tail, a list with components statistic, p.value, alternative, method, and probabilities.

Details

The result is a conditional probability under the supplied model. If prob was estimated from the same observations, the result is not by itself a calibrated exact test. The observed point is included in either tail. The package deliberately does not define a two-sided p-value.

Examples

x <- c(0, 1, 1, 0)
prob <- c(0.15, 0.40, 0.75, 0.60)
runs_tail(x, prob, tail = "upper")