Negative
The number of failures before the rth success in a sequence of independent Bernoulli trials with probability p of success on each trial. The range of this random variable is {0, 1, 2, ....}
Parameters
The success probability, must be in range (0,1)
The desired number of successes
an optional name/label
Properties
the desired number of successes to wait for
the probability of failure, 1-p
the probability of success, p
indicates whether pmf and cdf calculations are done by recursive (iterative) algorithm based on logarithms or via beta incomplete function and binomial coefficients.
the parameters for this type of random variable
Functions
Returns an array of probabilities each representing F(x_i). The CDF is evaluated for each point in the input array x and the probabilities are returned in the returned array.
Returns the probability of being in the interval, F(upper limit) - F(lower limit) Be careful, this is Pr{lower limit < = X < = upper limit} which includes the lower limit and has implications if the distribution is discrete
Returns the Pr{x1 <= X <= x2} for the distribution. Be careful, this is Pr{x1 <= X <= x2} which includes the lower limit and has implications if the distribution is discrete
Returns the F(x) = Pr{X <= x} where F represents the cumulative distribution function
Computes the cumulative probability distribution function for given value of failures
Computes the complementary cumulative probability distribution function for given value of x. This is P{X > x}
Computes the first order loss function for the function for given value of x, G1(x) = Emax(X-x,0)
Computes x_p where P(X <= x_p) = p for the supplied array of probabilities. Requires that the values within the supplied array are in (0,1)
Provides the inverse cumulative distribution function for the distribution
Gets the parameters as an array parameters0 is probability of success parameters1 is number of desired successes
Sets the parameters as an array parameters0 is probability of success parameters1 is number of desired successes
Returns the prob of getting x failures before the rth success where r is the desired number of successes parameter
If x is not an integer value, then the probability must be zero otherwise pmf(int x) is used to determine the probability
Computes the probabilities associated with the range and returns the value and the probability as a map with the integer value as the key and the probability as the related value.
Computes the 2nd order loss function for the distribution function for given value of x, G2(x) = (1/2)Emax(X-x,0)*max(X-x-1,0)
Returns the standard deviation for the distribution as the square root of the variance if it exists
Computes Pr{x < X } for the distribution.