good (version 1.0.1)

qgood: Quantile function for the Good distribution

Description

Quantile function for the Good distribution with parameters z and s.

Usage

qgood ( p , z , s , lower.tail = TRUE )

Arguments

p

vector of non-negative integer quantiles.

z

vector of first parameter for the Good distribution.

s

vector of second parameter for the Good distribution.

lower.tail

logical; if TRUE (default), probabilities are \(P(X \le x)\). Otherwise, \(P(X > x)\).

Value

The smallest integer x such that \(P(X \le x) \ge p\) (or such that \(P(X \le x) \ge 1-p\) if lower.tail is FALSE), where X is a random variable following a Good distribution with parameters z and s. Parameter z should be within the interval \((0,1)\), and parameter s in the reals. Vector p should have values between \(0\) and \(1\). If vector p has negative values and/or outside the interval \((0,1)\), qgood returns NaN with a warning. If vector p contains 1, qgood returns Inf. qgood calls dgood from package good.

References

Good, J. (1953). The population frequencies of species and the estimation of population parameters. Biometrika, 40: 237<U+2013>264.

Z<U+00F6>rnig, P. and Altmann, G. (1995). Unified representation of zipf distributions. Computational Statistics & Data Analysis, 19: 461<U+2013>473.

Kulasekera, K.B. and Tonkyn, D. (1992). A new distribution with applications to survival dispersal anddispersion. Communication in Statistics - Simulation and Computation, 21: 499<U+2013>518.

Doray, L.G. and Luong, A. (1997). Efficient estimators for the good family. Communications in Statistics - Simulation and Computation, 26: 1075<U+2013>1088.

Johnson, N.L., Kemp, A.W. and Kotz, S. Univariate Discrete Distributions. Wiley, Hoboken, 2005.

Kemp. A.W. (2010). Families of power series distributions, with particular reference to the lerch family. Journal of Statistical Planning and Inference, 140:2255<U+2013>2259.

Wood, D.C. (1992). The Computation of Polylogarithms. Technical report. UKC, University of Kent, Canterbury, UK (KAR id:21052).

See Also

See also polylog from copula, dgood, and pgood and rgood from good.

Examples

# NOT RUN {
# if p is not within [0, 1], NaN is returned with a warning
qgood ( p = c ( -0.6 , 1.3 ) , z = 0.5 , s = -3 )

# if z is not within 0 and 1, NaN is returned with a warning
qgood ( p = 0.5 , z = c(-0.6, -9, 0.5) , s = -3 )

qgood ( p = 0.5 , z = 0.6 , s = -3 )
qgood ( p = c ( 0.025 , 0.5 , 0.975 ) , z = 0.6 , s = -3 )
qgood ( p = c ( 0.025 , 0.5 , 0.975 ) , z = c ( 0.6 , 0.3 , 0.1 ) , s = -5 )
qgood ( p = c ( 0.025 , 0.5 , 0.975 ) , z = c ( 0.6 , 0.3 , 0.5 ) , s = -3 , lower.tail = FALSE )
qgood ( p = c ( 0.025 , 0.5 , 0.975 ) , z = c ( 0.6 , 0.3 ) , s = -3 )

# }