# tools:::Rd_package_title("bivgeom") tools:::Rd_package_description("bivgeom") package ## Details The DESCRIPTION file: tools:::Rd_package_DESCRIPTION("bivgeom") tools:::Rd_package_indices("bivgeom") ## Author(s) Alessandro Barbiero Maintainer: Alessandro Barbiero (alessandro.barbiero@unimi.it) ## References Roy, D. (1993) Reliability measures in the discrete bivariate set-up and related characterization results for a bivariate geometric distribution, Journal of Multivariate Analysis 46(2), 362-373. Barbiero, A. (2018) Properties and estimation of a bivariate geometric model with locally constant failure rates, submitted ## See Also `dbivgeomRoy`, `rbivgeomRoy`, `estbivgeomRoy`, `FbivgeomRoy` ## Examples ```r ##################################### #### MONTE CARLO SIMULATION PLAN #### ##################################### # setting the parameters' values theta1 <- 0.3 theta2 <- 0.7 theta3 <- 0.6 N <- 20 # number of Monte Carlo runs n <- 100 # sample size # arranging the array containig the simulation results # N runs, 7 methods, 3 estimates h <- array(0,c(N,7,3)) # setting the seed set.seed(12345) # function for handling missing values # when computing the mean and standard deviation of the estimates: meanrm <- function(x){mean(x,na.rm=TRUE)} sdrm <- function(x){sd(x,na.rm=TRUE)} colnames <- c("ML","MMP","MM1","MM2","MM3","MM4","LS") dimnames(h)[[2]] <- colnames # Monte Carlo simulation: for(i in 1:N) { d <- rbivgeomRoy(n,theta1,theta2,theta3) cat("MC run #",i,"\n") x<-d[,1] y<-d[,2] # implementing all the estimation methods # and saving the point estimates in the array h[i,1,] <- estbivgeomRoy(x, y, "ML") h[i,2,] <- estbivgeomRoy(x, y, "MMP") h[i,3,] <- estbivgeomRoy(x, y, "MM1") h[i,4,] <- estbivgeomRoy(x, y, "MM2") h[i,5,] <- estbivgeomRoy(x, y, "MM3") h[i,6,] <- estbivgeomRoy(x, y, "MM4") h[i,7,] <- estbivgeomRoy(x, y, "LS") } # printing MC expected values and standard errors # for each of the proposed estimation methods cat("hattheta1:","\n") cbind(mean=apply(h,c(2,3),meanrm)[,1],se=apply(h,c(2,3),sdrm)[,1]) cat("hattheta2:","\n") cbind(mean=apply(h,c(2,3),meanrm)[,2],se=apply(h,c(2,3),sdrm)[,2]) cat("hattheta3:","\n") cbind(mean=apply(h,c(2,3),meanrm)[,3],se=apply(h,c(2,3),sdrm)[,3]) # boxplots of MC distribution of the estimators of theta3 boxplot(h[,,3]) abline(h=theta3, lty=3) ```

bivgeom-package