Description Usage Arguments Value Examples

Assuming the log density of the chi-squared statistics admits a parametric form, this function estimates up to the fourth order log density derivatives.

1 | ```
density_LS(x)
``` |

`x` |
a sequence of chi-squared test statistics |

a list: the first-to-fourth log density derivatives

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
p = 1000
k = 7
# the prior distribution for lambda
alpha = 2
beta = 10
# lambda
lambda = rep(0, p)
pi_0 = 0.8
p_0 = floor(p*pi_0)
p_1 = p-p_0
lambda[(p_0+1):p] = stats::rgamma(p_1, shape = alpha, rate=1/beta)
# Generate a Poisson RV
J = sapply(1:p, function(x){rpois(1, lambda[x]/2)})
X = sapply(1:p, function(x){rchisq(1, k+2*J[x])})
out = density_LS(X)
``` |

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