in this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by jones [12] for length-biased data.the approach is based on the invariance principle for the empirical processes proved by horváth [10]. all simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by ...

the present study provides the data on the population parameters of an endemic qanat spirlin, alburnoides qanati from the endorheic kor river basin of iran to assess the stock status of this cyprinid fish species, which is highly important from management and conservation points of views. fish specimens (387) were collected from moshkan stream, kor river basin, iran in 2011-2012. asymptotic len...

In this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by Jones [12] for length-biased data.The approach is based on the invariance principle for the empirical processes proved by Horváth [10]. All simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by ...

length-biased data are widely seen in applications. they are mostly applicable in epidemiological studies or survival analysis in medical researches. here we aim to propose a berry-esseen type bound for the kernel density estimator of this kind of data.the rate of normal convergence in the proposed berry-esseen type theorem is shown to be o(n^(-1/6) ) modulo logarithmic term as n tends to infin...

Note that the symmetry property implies that the channel output coincides with the log-likelihood ratio `(y) = y. By this correspondence, symmetric densities admit a partial ordering by physical degradation Z1 Z2 if the corresponding chanels are ordered in the same way Q1 Q2 (i.e. Q1 is less noisy than Q2). Consider now belief propagation decoding with messages {hi→a}, {ĥa→i} and soft decisions...

This paper is evolved to have insight of Plankton-Nutrients interactions in the presence of delay in the growth term of phytoplankton species .The conditions for asymptotic stability about endemic equilibrium are derived in the absence of delay.The Nyquist criteria is used to estimate the length of delay to preserve stability .Analytic criterion for the existence of hopf-bifurcation is also dis...

Gallager and Van Voorhis have found optimal prefix-free codes κ(K) for a random variable K that is geometrically distributed: Pr[K = k] = p(1 − p) for k ≥ 0. We determine the asymptotic behavior of the expected length Ex[#κ(K)] of these codes as p → 0: Ex[#κ(K)] = log2 1 p + log2 log 2 + 2 + f ( log2 1 p + log2 log 2 )