fitdistrquantiles {HelpersMG}

Parameters of beta, normal or gamma distribution based on quantiles.

Description

Return the parameters of beta or gamm that fits the best the quantiles. The vector of probabilities can be obtained from names of quantiles.

Usage

fitdistrquantiles(
  quantiles = stop("At least two quantiles must be provided"),
  probs = NULL,
  scaled = FALSE,
  distribution = "beta"
)

Arguments

quantiles

Vector of quantiles.

probs

Numeric vector of probabilities with values in [0,1].

scaled

Used scaled least-square.

distribution

Distribution to be fitted: beta, normal, or gamma.

Details

fitdistrquantiles returns the parameters of beta, normal or gamma distribution

Value

Parameters of beta, normal or gamma distribution based on quantiles.

Author(s)

Marc Girondot [e-mail]

Examples

rd <- rbeta(100000, shape1 = 0.7, shape2 = 6.2, ncp=0)
(q <- quantile(rd, probs=c(0.025, 0.5, 0.975)))

(best <- fitdistrquantiles(quantiles = q, probs = c(0.025, 0.5, 0.975), 
                           scaled=FALSE, distribution = "beta"))
rd10000 <- rbeta(10000, shape1 = best["shape1"], shape2 = best["shape2"], ncp=best["ncp"])
quantile(rd10000, probs=c(0.025, 0.5, 0.975))

# Here the probabilities are obtained from names of quantiles
(best <- fitdistrquantiles(quantiles = q, scaled=FALSE, distribution = "beta"))
rd10000 <- rbeta(10000, shape1 = best["shape1"], shape2 = best["shape2"], ncp=best["ncp"])
quantile(rd10000, probs=c(0.025, 0.5, 0.975))

# If only two quantiles are provided, ncp cannot be fitted
(q2 <- quantile(rd, probs=c(0.025, 0.975)))
(best <- fitdistrquantiles(quantiles = q2, scaled=FALSE, distribution = "beta"))
rd10000 <- rbeta(10000, shape1 = best["shape1"], shape2 = best["shape2"])
quantile(rd10000, probs=c(0.025, 0.975))
x <- seq(from=0.00, to=1, by=0.001)
plot(x=x, y=pbeta(x, shape1 = best["shape1"], shape2 = best["shape2"]), 
     las=1, bty="n", type="l", ylim=c(0, 1))
segments(x0=q2[1], x1=q2[1], y0=0, y1=1, lty=2)
segments(x0=q2[2], x1=q2[2], y0=0, y1=1, lty=2)

(best <- fitdistrquantiles(quantiles = q, probs = c(0.025, 0.5, 0.975), 
                           scaled=FALSE, distribution = "gamma"))
rd10000 <- rgamma(10000, shape = best["shape"], scale = best["scale"])
quantile(rd10000, probs=c(0.025, 0.5, 0.975))

(best <- fitdistrquantiles(quantiles = c(10, 20, 30), probs = c(0.025, 0.5, 0.975), 
                           scaled=FALSE, distribution = "normal"))
rd10000 <- rnorm(10000, mean = best["mean"], sd = best["sd"])
quantile(rd10000, probs=c(0.025, 0.5, 0.975))