Description Usage Arguments Details Value Author(s) References See Also Examples
Random generation and density function for a finite mixture of univariate t-distribution.
1 2 3 4 |
n |
number of observations. |
x |
vector of quantiles. |
weight |
vector of probability weights, with length equal to number of components (k). This is assumed to sum to 1; if not, it is normalized. |
df |
vector of degrees of freedom (> 0, maybe non-integer). df = Inf is allowed. |
mean |
vector of means. |
sd |
vector of standard deviations. |
Sampling from finite mixture of t-distribution, with density:
Pr(x|\underline{w}, \underline{df}, \underline{μ}, \underline{σ}) = ∑_{i=1}^{k} w_{i} t_{df}(x| μ_{i}, σ_{i}),
where
t_{df}(x| μ, σ) = \frac{ Γ( \frac{df+1}{2} ) }{ Γ( \frac{df}{2} ) √{π df} σ } ≤ft( 1 + \frac{1}{df} ≤ft( \frac{x-μ}{σ} \right) ^2 \right) ^{- \frac{df+1}{2} }.
Generated data as an vector with size n.
Reza Mohammadi a.mohammadi@uva.nl
Mohammadi, A., Salehi-Rad, M. R., and Wit, E. C. (2013) Using mixture of Gamma distributions for Bayesian analysis in an M/G/1 queue with optional second service. Computational Statistics, 28(2):683-700, doi: 10.1007/s00180-012-0323-3
Mohammadi, A., and Salehi-Rad, M. R. (2012) Bayesian inference and prediction in an M/G/1 with optional second service. Communications in Statistics-Simulation and Computation, 41(3):419-435, doi: 10.1080/03610918.2011.588358
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ## Not run:
n = 10000
weight = c( 0.3, 0.5, 0.2 )
df = c( 4 , 4 , 4 )
mean = c( 0 , 10 , 3 )
sd = c( 1 , 1 , 1 )
data = rmixt( n = n, weight = weight, df = df, mean = mean, sd = sd )
hist( data, prob = TRUE, nclass = 30, col = "gray" )
x = seq( -20, 20, 0.05 )
densmixt = dmixt( x, weight, df, mean, sd )
lines( x, densmixt, lwd = 2 )
## End(Not run)
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