# Survival Distributions with piece-wise Constant Hazards and multiple states (function factories) Densitiy, distribution function, hazard function, cumulative hazard function and survival function of multi-state survival functions. Those functions return functions of one parameter that can be evaluated to give the density, distribution function, ... The parameters `t`, `Q`, `pi` and `abs` are checked only once and not at every function evaluation. ```r dmstate_fun(t, Q, pi, abs) pmstate_fun(t, Q, pi, abs) hmstate_fun(t, Q, pi, abs) chmstate_fun(t, Q, pi, abs) smstate_fun(t, Q, pi, abs) multistate_functions(t, Q, pi, abs) ``` ## Arguments - `t`: vector of left interval borders - `Q`: Q-matrices of the process, see details - `pi`: initial distribution - `abs`: indicator vector of absorbing states, see details ## Returns `dmstate_fun` gives the density. `pmstate_fun` gives the distribution function `hmstate_fun` gives the hazard function. `chmstate_fun` gives the cumulative hazard function. `smstate_fun` gives the survival function. `multistate_functions` gives an object of class "miniPCH" ## Functions * `dmstate_fun()`: density of survival distributions with piece-wise constant hazards and multiple states * `pmstate_fun()`: distribution function of survival distributions with piece-wise constant hazards and multiple states * `hmstate_fun()`: hazard function of survival distributions with piece-wise constant hazards and multiple states * `chmstate_fun()`: cumulative hazard function of survival distributions with piece-wise constant hazards and multiple states * `smstate_fun()`: survival function of survival distributions with piece-wise constant hazards and multiple states ## Examples ```r Tint <- 0 Q <- matrix( c( -0.3, 0.2, 0.1, 0 ,-0.4, 0.4, 0 , 0, 0 ), 3, 3, byrow = TRUE ) dim(Q) <- c(3,3,1) pi <- c(1,0,0) abs <- c(0,0,1) my_density <- dmstate_fun(Tint, Q, pi, abs) my_distribution <- pmstate_fun(Tint, Q, pi, abs) my_hazard <- hmstate_fun(Tint, Q, pi, abs) my_cumulative_hazard <- chmstate_fun(Tint, Q, pi, abs) my_survival <- smstate_fun(Tint, Q, pi, abs) t <- seq(0,20, by=0.1) par(mfrow=c(3,2)) plot(t, my_density(t), type="l") plot(t, my_distribution(t), type="l") plot(t, my_hazard(t), type="l", ylim=c(0,1)) plot(t, my_cumulative_hazard(t), type="l") plot(t, my_survival(t), type="l") Tint <- 0 Q <- matrix( c( -0.3, 0.2, 0.1, 0 ,-0.4, 0.4, 0 , 0, 0 ), 3, 3, byrow = TRUE ) dim(Q) <- c(3,3,1) pi <- c(1,0,0) abs <- c(0,0,1) my_obj <- multistate_functions(Tint, Q, pi, abs) t <- seq(0,20, by=0.1) plot(t, my_obj$d(t), type="l") ``` ## See Also dmstate

multistate_functions function