the empirical bayes estimators of treatment effects in a factorial experiment were derived and their asymptotic properties were explored. it was shown that they were asymptotically optimal and the estimator of the scale parameter had a limiting gamma distribution while the estimators of the factor effects had a limiting multivariate normal distribution. a bootstrap analysis was performed to ill...

Simulation of gamma and hadron showers in the energy range 100GeV- 25TeV has been carried out. For a big ideal Cherenkov light array, characteristics of lateral distribution of Cherenkov photon density have been studied. Results from this ideal detector are compared with those simulated for a real TUNKA- like array to investigate experimental potential of using existence of a hump in lateral di...

The maximum likelihood, moment and mixture of the estimators are derived for samples from the gamma distribution in the presence of outliers generated from gamma distribution. These estimators are compared empirically when all parameters are unknown; their bias and mean squares error are investigated with the help of numerical technique. We have shown that these estimators are asymptotically un...

Recent range expansions have probably occurred in many species, as they often happen after speciation events, after ice ages, or after the introduction of invasive species. While it has been shown that range expansions lead to patterns of molecular diversity distinct from those of a pure demographic expansion, the fact that many species do live in heterogeneous environments has not been taken i...

Heterotachy, the variation of substitution rate at a site across time, is a prevalent phenomenon in nucleotide and amino acid alignments, which may mislead probabilistic-based phylogenetic inferences. The covarion model is a special case of heterotachy, in which sites change between the "ON" state (allowing substitutions according to any particular model of sequence evolution) and the "OFF" sta...

A Fortran 90 module GammaCHI for computing and inverting the gamma and chi-square cumulative distribution functions (central and noncentral) is presented. The main novelty of this package are the reliable and accurate inversion routines for the noncentral cumulative distribution functions. Additionally, the package also provides routines for computing the gamma function, the error function and ...