Solve for Lambda for a Particular Mean Parametrized COM-Poisson Distribution

Source: R/comp_lambdas.R

Given a particular mean parametrized COM-Poisson distribution i.e. mu and nu, this function is used to find a lambda that can satisfy the mean constraint with a combination of bisection and Newton-Raphson updates. The function is also vectorized but will only update those that have not converged.

comp_lambdas(
  mu,
  nu,
  lambdalb = 1e-10,
  lambdaub = 1000,
  maxlambdaiter = 1000,
  tol = 1e-06,
  lambdaint = 1,
  summax = 100
)

comp_lambdas_fixed_ub(
  mu,
  nu,
  lambdalb = 1e-10,
  lambdaub = 1000,
  maxlambdaiter = 1000,
  tol = 1e-06,
  lambdaint = 1,
  summax = 100
)

Arguments

mu, nu

mean and dispersion parameters. Must be straightly positive.

lambdalb, lambdaub

numeric; the lower and upper end points for the interval to be searched for lambda(s).

maxlambdaiter

numeric; the maximum number of iterations allowed to solve for lambda(s).

tol

numeric; the convergence threshold. A lambda is said to satisfy the mean constraint if the absolute difference between the calculated mean and the corresponding mu values is less than tol.

lambdaint

numeric vector; initial gauss for lambda(s).

summax

maximum number of terms to be considered in the truncated sum

Value

Both comp_lambdas and comp_lambdas_fixed_ub returns the lambda value(s) that satisfies the mean constraint(s) as well as the current lambdaub value. lambda value(s) returns by comp_lambdas_fixed_ub is bounded by the lambdaub value. comp_lambdas has the extra ability to scale up/down lambdaub to find the most appropriate lambda values.