crossrunchange {crossrun}

Joint Distribution for Crossings and Runs, Varying Success Probability.

Description

Joint probability distribution for the number of crossings C and the longest run L in a sequence of n independent Bernoulli observations with p ossibly varying success probability. To enhance precision, results are stored in mpfr arrays and the probabilities are multiplied by m^{n-1} for a multiplier m.

Usage

crossrunchange(
  nmax = 100,
  prob = rep(0.5, 100),
  mult = 2,
  prec = 120,
  printn = FALSE
)

Arguments

nmax

max sequence length.

prob

success probabilities.

mult

multiplier for joint probabilities.

prec

mpft precision.

printn

logical for progress output.

Value

list pt of joint probabilities. Cumulative probabilities qt within each row are also included. Further, mostly for code checking, lists pat and qat conditional on starting with a success, and pbt and qbt conditional of starting with a failure, are included.

Examples

prob10 <- c(rep(.5,5),rep(.7,5))
crchange10 <- crossrunchange(nmax=10, prob=prob10,printn=TRUE)
print(crchange10$pt[[10]])