Description Usage Arguments Details Value Examples
Density, cumulative distribution function, quantile function and random number generation for the difference of two mixture distributions.
1 2 3 4 5 6 7 |
mix1 |
first mixture density |
mix2 |
second mixture density |
x |
vector of values for which density values are computed |
q |
vector of quantiles for which cumulative probabilities are computed |
lower.tail |
logical; if |
p |
vector of cumulative probabilities for which quantiles are computed |
n |
size of random sample |
If x_1 ~ f_1(x) and x_2 ~ f_2(x), the density of the difference x = x_1 - x_2 is given by the convolution
f(x) = \int f_1(x) f_2(x - u) du = (f_1 * f_2)(x).
The cumulative distribution function equates to
F(x) = \int F_1(x+u) f_2(u) du.
Both integrals are performed over the full support of the
densities and use the numerical integration function
integrate
.
Respective density, quantile, cumulative density or random numbers.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | # 1. Difference between two beta distributions, i.e. Pr( mix1 - mix2 > 0)
mix1 <- mixbeta(c(1, 11, 4))
mix2 <- mixbeta(c(1, 8, 7))
pmixdiff(mix1, mix2, 0, FALSE)
# Interval probability, i.e. Pr( 0.3 > mix1 - mix2 > 0)
pmixdiff(mix1, mix2, 0.3) - pmixdiff(mix1, mix2, 0)
# 2. two distributions, one of them a mixture
m1 <- mixbeta( c(1,30,50))
m2 <- mixbeta( c(0.75,20,50),c(0.25,1,1))
# random sample of difference
set.seed(23434)
rM <- rmixdiff(m1, m2, 1E4)
# histogram of random numbers and exact density
hist(rM,prob=TRUE,new=TRUE,nclass=40)
curve(dmixdiff(m1,m2,x), add=TRUE, n=51)
# threshold probabilities for difference, at 0 and 0.2
pmixdiff(m1, m2, 0)
mean(rM<0)
pmixdiff(m1,m2,0.2)
mean(rM<0.2)
# median of difference
mdn <- qmixdiff(m1, m2, 0.5)
mean(rM<mdn)
# 95%-interval
qmixdiff(m1, m2, c(0.025,0.975))
quantile(rM, c(0.025,0.975))
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