Compute the coefficients corresponding to the decomposition of some density in a given orthonormal polynomial basis.

orthoBasis_coef(
  data,
  comp.dist = NULL,
  comp.param = NULL,
  supp = c("Real", "Integer", "Positive", "Bounded.continuous"),
  degree,
  m = 3,
  other = NULL
)

Arguments

data

Observed sample from which the coefficients are calculated. Can be NULL if 'comp.dist' and 'comp.param' are specified.

comp.dist

(default to NULL) A list with two elements corresponding to component distributions (specified with R native names for these distributions) involved in the admixture model. Unknown elements must be specified as 'NULL' objects (for instance unknown 'f': list(f=NULL, g='norm')).

comp.param

(default to NULL) A list with two elements corresponding to the parameters of the component distributions, each element being a list itself. The names used in this list must correspond to the native R argument names for these distributions. Unknown elements must be specified as 'NULL' objects. For instance if 'f' is unknown: list(f = NULL, g = list(mean=0,sd=1)).

supp

Support of the density considered.

degree

Degree up to which the polynomial basis is built.

m

(default to 3) Only used when support is 'Integer'. Corresponds to the mean of the reference measure, i.e. Poisson(m).

other

(default to NULL) A list to precise bounds when the support is bounded, where the second and fourth elements give bounds.

Value

The list composed of 'degree' elements, each element being a numeric vector (with sample size) where each value represents the k-th order coefficient found when decomposing the density in the orthonormal polynomial basis.

Author

Xavier Milhaud xavier.milhaud.research@gmail.com

Examples

## Simulate data: sample1 <- rnorm(n = 7000, mean = 3, sd = 1) ## Compute the expansion coefficients in the orthonormal polynomial basis: coeff <- orthoBasis_coef(data = sample1, comp.dist = NULL, comp.param = NULL, supp = 'Real', degree = 3, m = 3, other = NULL) sapply(coeff, mean)
#> [1] 3.015972 6.439259 11.253154
## No observed data and decomposition of the known component of the admixture model: coeff <- orthoBasis_coef(data = NULL, comp.dist = list(NULL, 'norm'), comp.param=list(NULL,list(mean=3,sd=1)), supp = 'Real', degree=3, m=3, other = NULL) sapply(coeff, mean)
#> [1] 3.000558 6.365906 11.027697