crossrunauto: Joint Distribution for Crossings and Runs, autocorrelated...

In crossrun: Joint Distribution of Number of Crossings and Longest Run

Joint Distribution for Crossings and Runs, autocorrelated Sequence

Description

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

Usage

crossrunauto(
  nmax = 100,
  prob = 0.5,
  changeprob = 0.5,
  mult = 2,
  prec = 120,
  printn = FALSE
)

Arguments

nmax	max sequence length.
prob	success probability p.
changeprob	unrestricted change probability. If p ≥q 0.5, probability of changing to success, if not probability of changing to failure.
mult	multiplier for joint probabilities.
prec	mpft precision.
printn	logical for progress output.

Value

list of joint probabilities.

Examples

# p=0.6, independence
cr10.6 <- crossrunbin(nmax=10, prob=0.6, printn=TRUE)
cra10.6 <- crossrunauto(nmax=10, prob=0.6, changeprob=.6, printn=TRUE)
Rmpfr::asNumeric(cr10.6$pt[[10]])
Rmpfr::asNumeric(cr10.6$pt[[10]])
Rmpfr::asNumeric(cr10.6$pt[[10]]) - Rmpfr::asNumeric(cra10.6$pt[[10]]) # equal


# p=0.6, some dependence
cr10.6 <- crossrunbin(nmax=10, prob=0.6, printn=TRUE)
cra10.6.u.5 <- crossrunauto(nmax=10, prob=0.6, changeprob=.5, printn=TRUE)
round(Rmpfr::asNumeric(cr10.6$pt[[10]]),1)
round(Rmpfr::asNumeric(cra10.6.u.5$pt[[10]]),1) # not the same

crossrun documentation built on April 13, 2022, 9:05 a.m.