Pareto mixture distribution
Density, distribution function, quantile function and random generation for the Pareto mixture distribution with a equal to the shape of the first Pareto Distribution, b equal to the shape of the second Pareto Distribution and c is the mixture proportion. The locations and the scales parameters are equals to 0 and 1.
pparetomix(q, a = 1, b = 2, c = 0.75) dparetomix(x, a = 1, b = 2, c = 0.75) qparetomix(p, a = 1, b = 2, c = 0.75, precision = 10^(-10), initvalue = 0.5, Nmax = 1000) rparetomix(n, a = 1, b = 2, c = 0.75, precision = 10^(-10))
q |
a vector of quantiles. |
a |
the shape parameter of the first Pareto Distribution. |
b |
the shape parameter of the second Pareto Distribution. |
c |
the value of the mixture proportion. |
x |
a vector of quantiles. |
p |
a vector of probabilities. |
precision |
the precision of the Newton method. |
initvalue |
the initial value of the Newton method. |
Nmax |
the maximum of iteration done for the Newton method. |
n |
the number of observations. If length(n) > 1, the length is taken to be the number required. |
If the a, b and c are not specified, they respectively take the default values 1, 2 and 0.75.
The cumulative Pareto mixture distribution is
F(x) = c (1- x ^ {-a}) + ( 1 - c ) (1 - x ^ {-b}), x ≥ 1, a >0, b > 0, 0 ≤ c ≤ 1
where a and b are the shapes of the distribution and c is the mixture proportion.
dparetomix gives the density, pparetomix gives the distribution function, qparetomix gives the quantile function, and rparetomix generates random deviates.
The length of the result is determined by n for rparetomix, and is the maximum of the lengths of the numerical arguments for the other functions.
The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.
par(mfrow = c(3,1))
plot(function(x) dparetomix(x), 0, 5,ylab="density",
main = " Pareto mixture density ")
mtext("dparetomix(x)", adj = 0)
plot(function(x) pparetomix(x), 0, 5,ylab="distribution function",
main = " Pareto mixture Cumulative ")
mtext("pparetomix(x)", adj = 0)
plot(function(x) qparetomix(x), 0, 1,ylim=c(0,5),ylab="quantiles",
main = " Pareto mixture Quantile ")
mtext("qparetomix(x)", adj = 0)
#generate a sample of the Pareto mix distribution of size n
n <- 100
x <- rparetomix(n)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.