# Operations on SUNdistr-class objects Given an object of `SUNdistr-class`, or possibly two such things in some cases, the functions perform various operations, and produce a new object of the same class. package UTF-8 ```r affineTransSUNdistr(object, a, A, name, compNames, HcompNames, drop = TRUE) conditionalSUNdistr(object, comp, values, eventType = "=", name, drop = TRUE) convolutionSUNdistr(object1, object2, name, compNames, HcompNames) joinSUNdistr(object1, object2, name, compNames, HcompNames) marginalSUNdistr(object, comp, name, drop=TRUE) ``` ## Arguments - `object, object1, object2`: objects of class `SUNdistr` - `a`: a numeric vector; see Details - `A`: a numeric matrix; see Details - `name`: an optional character string with the name of the returned distribution - `compNames`: an optional vector of character strings with the names of the component variables of the returned distribution - `HcompNames`: an optional vector of character strings with the names of the hidden variables of the returned distribution - `drop`: a logical value (default: `TRUE`) relevant only in the case `m=1`. When both `m=1` and `drop=TRUE`, the returned object is of class either `SECdistrUv` or `SECdistrMv`, depending on the dimension of the returned object, and family `"SN"` or `"ESN"`, as appropriate. - `comp`: a vector of integers representing the selected components - `values`: a numeric vector which identifies the conditioning event - `eventType`: a single character value which indicates the type of the conditioning event, as described in the Details section; possible values are `"="` (default) and `">"` ## Details For an `object` which represents the distribution of a multivariate SUN random variable $Y$ of dimension `d`, say, a number of operations are possible, producing a new object of the same class. This `object` could have been created by `makeSUNdistr` or it could be the outcome from some previous call to one of the functions described here. The function `affineTransSUNdistr` computes the distribution of $a+A'Y$, provided `A` is a full-rank matrix with `nrow(A)=d` and `length(a)=ncol(A)`. See equation (7.6) of Azzalini & Capitanio (2014). The function `marginalSUNdistr` builds a SUN distribution from the components selected by the `comp` vector. A conditional distribution can be computed using `conditionalSUNdistr` for two type of events, selected by `eventType`. The `"="` case corresponds to the event $Y₁=y₁$ where $Y₁$ is the subset of components identified by the `comp` argument, $y₁$ is vector specified by the `values` argument and the equality sign must hold for each component. See equation (7.6) of Azzalini & Capitanio (2014). If `conditionalSUNdistr` is used with `eventType=">"`, the conditiong refers to the event $Y₁>y₁$, where the inequality must be interpreted components-wise; see Arellano-Valle & Azzalini (2021) for the underlying mathematical result. If the conditional distribution is required for the reverse inequality condition, `"<"` say, this is equivalent to consideration of the event $-Y₁>-y₁$. The corresponding distribution can be obtained in two steps: first a new variable is constructed reversing the sign of the required components using `affineTransSUNdistr`; then `conditionalSUNdistr` is applied to this new variable with the `">"` condition and values $-y₁$. More complex conditions, where the `"<"` and `">"` signs are mixed for different component varables, can be handled similarly, by introducing a square matrix `A` for `affineTransSUNdistr` having an appropriate combination of `1`s' and `-1`'s on its main diagonal, and 0's elsewhere, and matching changes of sign to the components of $y₁$. Functions `convolutionSUNdistr` and `joinSUNdistr` operate under the assumptions that `object1` and `object2` refer to independent variables. Specifically, `convolutionSUNdistr` computes the convolution of the two objects (i.e. the distribution of the sum of two independent variables), which must have the same dimension `d`. Function `joinSUNdistr` combines two objects into a joint distribution. If the arguments `name`, `compNames` and `HcompNames` are missing, they are composed from the supplied arguments. ## Returns an object of `SUNdistr-class` ## References Arellano-Valle, R. B. and Azzalini, A. (2021). Some properties of the unified skew-normal distribution. **Statistical Papers**, tools:::Rd_expr_doi("https://doi.org/10.1007/s00362-021-01235-2") and [arXiv:2011.06316](https://arxiv.org/abs/2011.06316) Azzalini, A. with the collaboration of Capitanio, A. (2014). **The Skew-Normal and Related Families**. Cambridge University Press, IMS Monographs series. ## Author(s) Adelchi Azzalini ## Note The present structure and user interface of this function, and of other ones related to the SUN distribution, must be considered experimental, and they might possibly change in the future. ## See Also `SUNdistr-base`, `makeSUNdistr`, `SUNdistr-class` ## Examples ```r xi <- c(1, 0, -1) Omega <- matrix(c(2,1,1, 1,3,1, 1,1,4), 3, 3) Delta <- matrix(c(0.72,0.20, 0.51,0.42, 0.88, 0.94), 3, 2, byrow=TRUE) Gamma <- matrix(c(1, 0.8, 0.8, 1), 2, 2) dp3 <- list(xi=xi, Omega=Omega, Delta=Delta, tau=c(-0.5, 0), Gamma=Gamma) sun3 <- makeSUNdistr(dp=dp3, name="SUN3", compNames=c("x", "w", "z")) # a <- c(1,-2) A <- matrix(1:6, 3, 2) sun2at <- affineTransSUNdistr(sun3, a, A, "SUN2at", compNames=c("at1", "at2")) sun2m <- marginalSUNdistr(sun3, comp=c(1,3), name="SUN2m") sun1c <- conditionalSUNdistr(sun3, comp=c(1,3), values=c(1.1, 0.8), eventType=">", name="SUN1c", drop=FALSE) # Omega <- matrix(c(5, 1, 1, 6), 2, 2) Delta <- matrix(c(0.30, 0.50, 0.50, 0.85), 2, 2, byrow=TRUE) Gamma <- matrix(c(1, 0.18, 0.18, 1), 2, 2) tau <- c(0.4, -0.8) dp2 <- list(x=c(1, 0), Omega=Omega, Delta=Delta, tau=tau, Gamma=Gamma) sun2 <- makeSUNdistr(dp=dp2, name="SUN2", compNames=c("u", "v")) # sun2conv <- convolutionSUNdistr(sun2, sun2m, name="SUN2sum") sun5 <- joinSUNdistr(sun3, sun2) ```

SUNdistr-op function