pgood {good}

Distribution function for the Good distribution

Description

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

Usage

pgood ( q , z , s , lower.tail = TRUE )

Arguments

q

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

pgood returns the cumulative distribution function (cdf) for the Good distribution with parameters z and s. Parameter z should be within the interval (0,1), and parameter s in the reals. If q is non-integer, pgood returns the cdf of floor(q) with a warning. If q is negative, pgood returns 0 with a warning. pgood calls dgood from package good.

Author(s)

Jordi Tur, David Moriña, Pere Puig, Alejandra Cabaña, Argimiro Arratia, Amanda Fernández-Fontelo

References

Good, J. (1953). The population frequencies of species and the estimation of population parameters. Biometrika, 40: 237–264.

Zörnig, P. and Altmann, G. (1995). Unified representation of zipf distributions. Computational Statistics & Data Analysis, 19: 461–473.

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

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

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, 140:2255–2259.

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 qgood and rgood from good.

Examples

# if q < 0, pgood returns NaN with a warning
pgood ( q = -3 , z = 0.6 , s = -3  )

# if q is non-integer, pgood returns the cdf of floor(q) with a warning
pgood ( q = 3.4 , z = 0.6 , s = -3 )

# if z is not within 0 and 1, pgood returns returns NaN with a warning
pgood ( q = 3.4 , z = c( -0.6 , 0.6) , s = -3 )

pgood ( q = 0 : 2 , z = 0.6 , s = -3 )
pgood ( q = 0 : 1 , z = c ( 0.6 , 0.9 ) , s = -3 )
pgood ( q = 0 : 1 , z = c ( 0.6 , 0.9 ) , s = -3 , lower.tail = FALSE )
pgood ( q = 0 : 2 , z = c ( 0.6 , 0.9 ) , s = c ( -3 , -4 , -5 ) )