mvClaim: Multivariate general insurance claims modelling

Description Usage Arguments Value Examples

Mixture of bivariate gamma regressions, or model-based clustering with bivariage gamma distributions and covariates, for various parsimonious model types. Models are estimated by EM algorithm.

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MBGR(modelName = c("VC", "VI", "VV", "VE", "CV", "IV", "EV", "EC", "CE"),
  y, data, G, f1, f2, f3, f4, gating, initialization = "mclust",
  maxit = 200, tol = 1e-05, verbose = TRUE)

`modelName`	A character string indicating which model to be fitted. Need to be one of "EE", "EI", "IE".
`y`	A vector of character strings indicating which variables in the data are treated as response or dependent variables.
`data`	A matrix or data frame of observations. Categorical variables are allowed as covariates.
`G`	An interger vector specifying the number of mixture components (clusters).
`f1`	A regression formula for the α_1 parameter in the bivariate gamma distribution. Note that, depending on the model type, might not be necessary to provide it.
`f2`	A regression formula for the α_2 parameter in the bivariate gamma distribution. Note that, depending on the model type, might not be necessary to provide it.
`f3`	A regression formula for the α_3 parameter in the bivariate gamma distribution. Note that, depending on the model type, might not be necessary to provide it.
`f4`	A regression formula for the β parameter in the bivariate gamma distribution. Note that, depending on the model type, might not be necessary to provide it.
`gating`	Specifies the gating network in the MoE model, can be "C", "E" or a regression formula.
`initialization`	Specifies initialization method for EM algorithm. The default is "`mclust`".
`maxit`	A parameter that controls the number of maximum iteration in the EM algorithm. The default is 100.
`tol`	A parameter that controls the convergence tolerance in the EM algorithm. The default is 1e-5.
`verbose`	A logical controlling whether estimations in each EM iteration are shown in the fitting process. The default is TRUE.

An object of class BGR providing the estimation results. The details of the output components are:

`call`	The matched call.
`expert.coef`	The estimated coefficients in the expert network, if exists.
`gating.coef`	The estimated coefficients in the gating network, if exists.
`alpha1`	The estimated alpha1 values.
`alpha2`	The estimated alpha2 values.
`alpha3`	The estimated alpha3 values.
`beta`	The estimated beta values.
`pro`	A vector whose g-th component is the mixing proportion for the g-th component of the mixture model.
`z`	A matrix whose [i,g]-th entry is the probability that observation i in the data belongs to the g-th group.
`class`	The classification corresponding to z.
`fitted.values`	The fitted values of the regression.
`residuals`	The residuals of the regression
`loglike`	The final estimated maximum log-likelihood value.
`ll`	The sequence of log-likelihood values in the EM algorithm fitting process.
`df`	The number of estimated parameters.
`AIC`	AIC values.
`BIC`	BIC values.
`Hessian`	The Hessian matrix at the estimated values
`iter`	Total iteration numbers.
`formula`	The formulas used in the regression.
`y`	The input response data.
`n`	The number of observations in the data.
`gating.model`	The binomial/multinomial regression model in the gating network.
`Model.Matrix`	The used model matrix for each regression formula.

m1 <- MBGR(modelName = "VV",
           y=c("y1","y2"), data = fullsim, G=2,
           f1     = ~ w1 + w2,
           f2     = ~ w2 + w3,
           f3     = ~ w1 + w2 + w3,
           f4     = ~ w1 + w2 + w3,
           gating = "C",
           verbose = FALSE)