Description Usage Arguments Details Value Note Author(s) References See Also Examples
Density, distribution function, quantile function and random
generation for the Bernoulli-Gamma distribution with parameters
prob
, shape
, and scale
.
1 2 3 4 | dberngamma(x, prob, scale, shape)
pberngamma(q, prob, scale, shape)
qberngamma(p, prob, scale, shape)
rberngamma(n, prob, scale, shape)
|
x,q |
vector of quantiles. |
p |
vector of probabilities. |
prob |
probability of non-zero event. |
n |
number of random samples. |
scale,shape |
shape and scale parameters of the gamma distribution. |
Mixture of the Bernoulli and the Gamma distribution. The Bernoulli
distribution is used to model the occurrence of zero values with the
probability of 1-prob
. Non-zero values follow the Gamma
distribution with shape
and scale
parameters.
The probability density function (PDF) is defined as:
g(x) = if(x > 0) pi*gamma(x) else 1-pi
where gamma(x) is the probability density function of the gamma distribution and π is probability of a non-zero event.
The cumulative distribution function (CDF) is defined as:
G(x) = if(x > 0) 1- pi + pi*Gamma(x) else 1-pi
where Gamma(x) is the cumulative distribution function of the gamma distribution.
The quantile function (inverse of the CDF) is defined as
G^{-1}(x) = if(p > 1-p) Gamma^{-1}((p-1+pi)/pi) else 0
where Gamma^{-1}(p) is the inverse CDF of the gamma distribution and p is a probability.
dberngamma
gives the density (pdf), pberngamma
gives
the distribution function (cdf), qberngamma
gives the
quantile function (inverse cdf), and rberngamma
generates
random deviates.
The implementation is largely based on the bgamma
family in
the CaDENCE
-package (Cannon, 2012) that was only available as
test version at time of implementation (Mar. 2012). The
CaDENCE
-package is available at
http://www.eos.ubc.ca/~acannon/CaDENCE/.
For further details and meteorological application of Bernoulli-Gamma distributions (also referred to as 'Mixed Gamma' distribution) see Burger et al. 2012, Cannon 2008, Li et al. 2010, Mooley 1973, Piani et al. 2010, Thom 1968, Sloughter et al. 2007.
Lukas Gudmundsson
Burger, G.; Murdock, T. Q.; Werner, A. T.; Sobie, S. R. & Cannon, A. J. Downscaling extremes - an intercomparison of multiple statistical methods for present climate. Journal of Climate, American Meteorological Society, early online release, 2012, doi:10.1175/JCLI-D-11-00408.1.
Cannon, A. J. Probabilistic Multisite Precipitation Downscaling by an Expanded Bernoulli-Gamma Density Network. Journal of Hydrometeorology, American Meteorological Society, 2008, 9, 1284-1300, doi:10.1175/2008JHM960.1.
Cannon, A. J. Neural networks for probabilistic environmental prediction: Conditional Density Estimation Network Creation and Evaluation (CaDENCE) in R. Computers & Geosciences, 2012, 41, 126 - 135, doi:10.1016/j.cageo.2011.08.023.
Li, H.; Sheffield, J. & Wood, E. F. Bias correction of monthly precipitation and temperature fields from Intergovernmental Panel on Climate Change AR4 models using equidistant quantile matching. J. Geophys. Res., AGU, 2010, 115, D10101, doi:10.1029/2009JD012882.
Mooley, D. A. Gamma Distribution Probability Model for Asian Summer Monsoon Monthly Rainfall. Monthly Weather Review, 1973, 101, 160-176, doi:10.1175/1520-0493(1973)101<0160:GDPMFA>2.3.CO;2.
Piani, C.; Haerter, J. & Coppola, E. Statistical bias correction for daily precipitation in regional climate models over Europe. Theoretical and Applied Climatology, 2010, 99, 187-192, doi:10.1007/s00704-009-0134-9.
Thom, H. C. S. Approximate convolution of the gamma and mixed gamma distributions. Monthly Weather Review, 1968, 96, 883-886, doi:10.1175/1520-0493(1968)096<0883:ACOTGA>2.0.CO;2.
Sloughter, J. M. L.; Raftery, A. E.; Gneiting, T. & Fraley, C. Probabilistic Quantitative Precipitation Forecasting Using Bayesian Model Averaging. Monthly Weather Review, 2007, 135, 3209-3220, doi:10.1175/MWR3441.1.
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 | data(obsprecip)
(ts <- startberngamma(obsprecip[,1]))
hist(obsprecip[,1],freq=FALSE)
lines(seq(0,20),dberngamma(0:20,
prob=ts$prob,
scale=ts$scale,
shape=ts$shape),
col="red")
pp <- seq(0.01,0.99,by=0.01)
qq <-quantile(obsprecip[,1],probs=pp)
plot(qq,pp)
lines(qberngamma(pp,
prob=ts$prob,
scale=ts$scale,
shape=ts$shape),
pp,col="red")
plot(qq,pp)
lines(qq,
pberngamma(qq,
prob=ts$prob,
scale=ts$scale,
shape=ts$shape),
col="red")
hist(rberngamma(1000,
prob=ts$prob,
scale=ts$scale,
shape=ts$shape),freq=FALSE)
|
Loading required package: fitdistrplus
Loading required package: MASS
Loading required package: survival
$prob
[1] 0.4758602
$scale
[1] 9.328407
$shape
[1] 0.5020363
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