# cdfBinomialInv¶

## Purpose¶

Computes the binomial quantile or inverse cumulative distribution function.

## Format¶

s = cdfBinomialInv(p, trials, prob)
Parameters: p (NxK matrix, Nx1 vector or scalar) – Probabilities at which to compute the inverse of the Binomial cumulative distribution function. $$0 \lt p \lt 1$$. trials (LxM matrix) – ExE conformable with p. $$trials > 0$$. prob (PxQ matrix) – The probability of success on any given trial. ExE conformable with p. $$0 < prob < 1$$. s (NxK matrix, Nx1 vector or scalar) – The number of successes.

## Examples¶

What is a reasonable range of wins for a basketball team playing 82 games in a season, with a 60% chance of winning any game? For our example we will define a reasonable range as falling between the top and bottom deciles.

// Probability range
range = { .10, .9 };

// Number of trials
trials = 82;

// Probabiliy of success
prob = 0.6

// Call cdfBinomialInv
s = cdfBinomialInv(range, trials, prob);
print       "s = "  s;

After above code,

s =
43
55

This means that a team with a 60% chance of winning any one game would win between 43 and 55 games in 80% of seasons.

## Remarks¶

For invalid inputs, cdfBinomialInv() will return a scalar error code which, when its value is assessed by function scalerr(), corresponds to the invalid input. If the first input is out of range, scalerr() will return a 1; if the second is out of range, scalerr() will return a 2; etc.