YEAB (version 1.0.6)

fleshler_hoffman: Fleshler & Hoffman (1962) progression

Description

This function calculates the values of intervals approximately for an exponential distribution, but avoiding extremely large values.

Usage

fleshler_hoffman(N, VI)

Value

A vector of calculated values for the intervals.

Arguments

N

The total number of intervals.

VI

The value of the Variable Interval

Details

This function calculates the values of intervals approximately for a exponential distribution, but avoiding extremely large values which can produce extinction. It uses the formula derived from the Fleshler & Hoffman article, where the first factor of the equation is -log(1 - p)^(-1), representing the expected value or mean of the intervals. This value is also the inverse of a Poisson process, 1/lambda. Since we want the expected value or mean to be the value of the IV, we replace that constant with VI. The function handles the case when n = N, where the value becomes undefined (log(0)), by using L'Hopital's rule to find the limit of the function as n approaches N. The resulting values are then multiplied by the IV and the logarithm of N to obtain the final calculated values.

References

Fleshler, M., & Hoffman, H. S. (1962). A progression for generating variable-interval schedules. Journal of the Experimental Analysis of Behavior, 5(4), 529-530.

Examples

# Calculate intervals for N = 10, and IV = 30
N <- 15
iv <- 90
intervals <- round(fleshler_hoffman(N,iv), 3)
# Plot the intervals and the exponential distribution corresponding to the
# same mean (IV)
hist(intervals, freq = FALSE)
curve(dexp(x, rate = 1/iv), add = TRUE, col = 'red')
legend('topright', legend = c('F&H', 'Exponential'), lty = 1, col = c('black', 'red'))