genUVLambda: Generation of three-dimensional random deviates.

In MobilePhoneESSnetBigData/pestim: Population Estimations Using Mobile Phone Data

Description

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

\int_{0}^{∞}dλ f_{λ}(λ)\int_{0}^{∞}dv f_{v}(v) \int_{0}^{∞} f_{u}(u)\ Φ(u\cdot v, (1 - u) \cdot v; λ, N^{\textrm{MNO}}, N^{\textrm{Reg}})\mathbb{P}(N^{\textrm{MNO, rep}}\big| u,v,λ).

The Monte Carlo technique makes use of stratified importance sampling.

Usage

genUVLambda(nSim, nStrata, fu, fv, flambda, nMNO)

Arguments

nSim	number of three-dimensional points to generate
nStrata	integer vector of length 3 with the number of strata in each dimension
fu	named list with the prior marginal distributions of the parameter u
fv	named list with the prior marginal distributions of the parameter v
flambda	named list with the prior marginal distributions of the parameter λ
nMNO	non-negative integer vector with the number of individuals according to the MNO

Details

Notice that nSim points are generated for each of the length(nMNO) cells so that the final data.table has nSim\timeslength(nMNO) rows.

The prior distributions are specified as named lists where the first component of each list must be the name of distribution ('unif', 'triang', 'gamma') and the rest of 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.

• triang: xMin, xMax, xMode for minimum, maximum and mode (see qtriang).

• gamma: scale and shape with the same meaning as in rgamma.

Value

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

• The length of nMNO identifies the number of territorial cells in which the number of individuals detected by the telecommunication network. The column cellID identifies these territorial cells.

• Stratum_u, Stratum_v, and Stratum_lambda jointly identify each stratum in which the region of integration has been divided with the stratification.

See Also

genUV

Examples

# This data.table must have 10x5x3= 150 rows and only one stratum
genUVLambda(nSim = 1000, nStrata = c(1, 2, 5),
      fu = list('unif', xMin = 0.3, xMax = 0.5), 
      fv = list('gamma', shape = 11, scale = 97 / 10),
      flambda = list('gamma', shape = 2, scale = 97 / 1),
      nMNO = c(20, 17, 25))
      

MobilePhoneESSnetBigData/pestim documentation built on May 31, 2019, 2:44 p.m.