genUV: Generation of two-dimensional random deviates.
In MobilePhoneESSnetBigData/pestim: Population Estimations Using Mobile Phone Data

Description Usage Arguments Details Value See Also Examples

Generate two-dimensional random deviates for a Monte Carlo computation of the integral

\int_{0}^{∞}dv f_{2}(v)\int_{0}^{∞} f_{1}(u)\ Φ(u\cdot v, (1 - u) \cdot v; λ, N^{\textrm{MNO}}, N^{\textrm{Reg}}).

The Monte Carlo technique makes use of stratified importance sampling.

1	genUV(nSim, nStrata, f1, f2, lambda, nMNO, nReg)

`nSim`	number of two-dimensional points to generate
`nStrata`	integer vector of length 2 with the number of strata in each dimension
`f1,`	f2 named lists with the prior marginal distributions of the two-dimensional points
`lambda`	numeric vector
`nMNO,`	nReg non-negative integer vectors

The lengths of the input vectors nMNO and nReg must be equal and independent of the length of the input vector lambda. Notice that nSim points are generated for each of the length(nMNO)\timeslength(lambda) combinations so that the final data.table has nSim\timeslength(nMNO) \timeslength(lambda) rows.

The prior distributions are specified as named lists where the first component of each list must be the name of distribution ('unif', 'triang', 'degen', 'gamma') and the rest components must be named according to the name of the parameters of the random generator of the corresponding distribution according to:

unif: xMin, xMax for the minimum, maximum of the sampled interval.
degen: x0 for the degenerate value of the random variable.
triang: xMin, xMax, xMode for minimum, maximum and mode (see qtriang).
gamma: scale and shape with the same meaning as in rgamma.

genUV returns a data.table with the (u,v) coordinates of each point together with additional variables:

The common length of nMNO and nReg identifies the number of territorial cells in which the number of individuals detected by the telecommunication network and official data. The column cellID identifies these territorial cells.
The length of lambda identifies the number of parameters upon which the integral will be computed in each cell. The column parID identifies each of these input parameters.
Stratum_u and Stratum_v jointly identify each stratum in which the region of integration has been divided with the stratification.

runif, qtriang, rgamma for related functions.

# This data.table must have 10x5x3= 150 rows and only one stratum
genUV(nSim = 10, nStrata = c(1, 1),
      f1 = list('unif', xMin = 0.3, xMax = 0.5), f2 = list('gamma', shape = 11, scale = 12),
      lambda = seq(0, 1, length.out = 5),
      nMNO = c(20, 17, 25), nReg = c(115, 123, 119))