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Density, distribution function, quantile function and random generation for the logarithmic series distribution.
dlgser(x, theta, log = FALSE)plgser(q, theta, lower.tail = TRUE, log.p = FALSE)
qlgser(p, theta, lower.tail = TRUE, log.p = FALSE)
rlgser(n, theta)
vector of quantiles.
vector; concentration parameter; (0 < theta < 1
).
logical; if TRUE, probabilities p are given as log(p).
logical; if TRUE (default), probabilities are
vector of probabilities.
number of observations. If length(n) > 1
,
the length is taken to be the number required.
Probability mass function
Cumulative distribution function
Quantile function and random generation are computed using algorithm described in Krishnamoorthy (2006).
Krishnamoorthy, K. (2006). Handbook of Statistical Distributions with Applications. Chapman & Hall/CRC
Forbes, C., Evans, M. Hastings, N., & Peacock, B. (2011). Statistical Distributions. John Wiley & Sons.
x <- rlgser(1e5, 0.66)
xx <- seq(0, 100, by = 1)
plot(prop.table(table(x)), type = "h")
lines(xx, dlgser(xx, 0.66), col = "red")
# Notice: distribution of F(X) is far from uniform:
hist(plgser(x, 0.66), 50)
xx <- seq(0, 100, by = 0.01)
plot(ecdf(x))
lines(xx, plgser(xx, 0.66), col = "red", lwd = 2)
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