# Pairwise Scatter Plots and Histograms for Finite Mixture of Multivariate Distributions. It plots the scatter plots with density contours for different multivariate distributions. Possible options are the Skew-normal (`family == "SN"`), Normal (`family == "Normal"`) and Student-t (`family == "t"`) distribution. Different colors are used by groups. Histograms are shown in the diagonal. ```r rMMSN.contour(model = NULL, y = NULL, mu = NULL, Sigma = NULL, shape = NULL, nu = NULL, pii = NULL, Zij = NULL, contour = FALSE, hist.Bin = 30, contour.Bin = 10, slice = 100, col.names = NULL, length.x = c(0.5, 0.5), length.y = c(0.5, 0.5), family = "SN") ``` ## Arguments - `model`: is an object resultant from the `fit.FMMSNC` function. - `y`: the response matrix with dimension $n$x$p$. - `mu`: a list with $g$ entries, where each entry represents location parameter per group, being a vector of dimension $p$. - `Sigma`: a list with $g$ entries, where each entry represents a scale parameter per group, a matrix with dimension $p$x$p$. - `shape`: a list with $g$ entries, where each entry represents a skewness parameter, being a vector of dimension $p$. - `nu`: the degrees of freedom for the Student-t distribution case, being a vector with dimension $g$. - `pii`: a vector of weights for the mixture of dimension $g$, the number of clusters. It must sum to one! - `Zij`: a matrix of dimension $n$x$p$ indicating the group for each observation. - `contour`: If `contour == TRUE` the density contour will be shown, if `contour == FALSE` the density contour must be not returned. - `hist.Bin`: number of bins in the histograms. Default is 30. - `contour.Bin`: creates evenly spaced contours in the range of the data. Default is 10. - `slice`: desired length of the sequence for the variables grid. This grid is build for the contours. - `col.names`: names passed to the data matrix $y$ of dimension $p$. - `length.x`: a vector of dimension 2 with the value to be subtracted and added from the minimum and maximum observation in the x-axis respectively. Default is `c(0.5,0.5)`. - `length.y`: a vector of dimension 2 with the value to be subtracted and added from the minimum and maximum observation in the y-axis respectively. Default is `c(0.5,0.5)`. - `family`: distribution family to be used. Available distributions are the Skew-normal ("SN"), normal ("Normal") or Student-t ("t") distribution. ## Details If the `model` object is used, the user still has the option to choose the `family`. If the `model` object is not used, the user must input all other parameters. User may use the `rMMSN` function to generate data. ## References Cabral, C. R. B., Lachos, V. H., & Prates, M. O. (2012). Multivariate mixture modeling using skew-normal independent distributions. Computational Statistics & Data Analysis, 56(1), 126-142. Prates, M. O., Lachos, V. H., & Cabral, C. (2013). mixsmsn: Fitting finite mixture of scale mixture of skew-normal distributions. Journal of Statistical Software, 54(12), 1-20. C.E. Galarza, L.A. Matos, D.K. Dey & V.H. Lachos. (2019) On Moments of Folded and Truncated Multivariate Extended Skew-Normal Distributions. Technical report. ID 19-14. University of Connecticut. F.H.C. de Alencar, C.E. Galarza, L.A. Matos & V.H. Lachos. (2019) Finite Mixture Modeling of Censored and Missing Data Using the Multivariate Skew-Normal Distribution. echnical report. ID 19-31. University of Connecticut. ## Author(s) Francisco H. C. de Alencar hildemardealencar@gmail.com , Christian E. Galarza cgalarza88@gmail.com , Victor Hugo Lachos hlachos@uconn.edu and Larissa A. Matos larissam@ime.unicamp.br Maintainer: Francisco H. C. de Alencar hildemardealencar@gmail.com ## Note This functions works well for any length of $g$ and $p$, but contour densities are only shown for $p = 2$. ## See Also `fit.FMMSNC`, `rMMSN` and `fit.FMMSNC` ## Examples ```r mu <- Sigma <- shape <- list() mu[[1]] <- c(-3,-4) mu[[2]] <- c(2,2) Sigma[[1]] <- matrix(c(3,1,1,4.5), 2,2) Sigma[[2]] <- matrix(c(2,1,1,3.5), 2,2) shape[[1]] <- c(-2,2) shape[[2]] <- c(-3,4) nu <- 0 pii <- c(0.6,0.4) percent <- c(0.1,0.2) n <- 100 seed <- 654678 set.seed(seed) test = rMMSN(n = n, pii = pii,mu = mu,Sigma = Sigma,shape = shape, percent = percent, each = TRUE, family = "SN") ## SN ## SN.contour = rMMSN.contour(model = NULL, y = test$y, Zij = test$G ,mu = mu, Sigma = Sigma, shape = shape, pii = pii, family = "SN") #Plotting contours may take some time... ## SN ## SN.contour = rMMSN.contour(model = NULL, y = test$y, Zij = test$G ,mu = mu, Sigma = Sigma, shape = shape, pii = pii, contour = TRUE, family = "SN") ## Normal ## N.contour = rMMSN.contour(model = NULL,y = test$y, Zij = test$G ,mu = mu, Sigma = Sigma, shape = shape, pii = pii, contour = TRUE, family = "Normal") ## t ## t.contour = rMMSN.contour(model = NULL,y = test$y, Zij = test$G ,mu = mu, Sigma = Sigma, shape = shape, pii = pii, nu = c(4,3), contour = TRUE, family = "t") ```

rMMSN.contour function