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Continuous cover forests contain large numbers of spatially distributed trees of different sizes. The growth of a particular tree is a function of the properties of that tree and the neighbor trees, since they compete for light, water and nutrients. Such a dynamical system is highly nonlinear and multidimensional. In this paper, a particular tree is instantly harvested if a control function based on two local state variables, S and Q, is satisfied, where S represents the size of the particular tree and Q represents the level of local competition. The control function has two parameters. An explicit nonlinear present value function, representing the total value of all forestry activities over time, is defined. This is based on the parameters in the control function, now treated as variables, and six new parameters. Explicit functions for the optimal values of the two parameters in the control function are determined via optimization of the present value function. Two equilibria are obtained, where one is a unique local maximum and the other is a saddle point. An equation is determined that defines the region where the solution is a unique local maximum. Then, a case study with a continuous cover Picea abies forest, in southern Sweden, is presented. A new growth function is estimated and used in the simulations. The following procedure is repeated for five alternative levels of the interest rate: The total present value of all forest management activities in the forest, during 300 years, is determined for 1000 complete system simulations. In each system simulation, different random combinations of control function parameters are used and the total present value of all harvest activities is determined. Then, the parameters of the present value function are estimated via multivariate regression analysis. All parameters are determined with high precision and high absolute t-values. The present value function fits the data very well. Then, the optimal control function parameters and the optimal present values are analytically determined for alternative interest rates. The optimal solutions found within the relevant regions are shown to be unique maxima and the solutions that are saddle points are located far outside the relevant regions.

Aly and Benkherouf (2011) introduced a new method for generating a new class of distributions based on the probability generating function. Here we consider the Harris extended Burr XII distribution and explore their properties. Moments, quantiles, etc are derived. The model parameters are estimated by maximum likelihood method. Simulation is done to see the behavior of maximum likelihood estimates. Application is given to a real life data sets to compare our model with other computative models.

KEYWORDS:  Sections; Harris distribution; Harris Extended Burr XII distribution; Hazard rate function; Marshall-Olkin family of distribution; Order statistics; Quantile function; Survival function.

In this paper we develop approximate Bayes estimators of the shape parameters of the generalized inverted Kumaraswamy (GIKum) distribution based on the progressive first-failure censored plan. We consider the maximum likelihood and Bayesian estimations with gamma-informative prior distribution for the parameters, reliability function, hazard rate and reversed hazard rate functions. We apply the Lindley’s approximation and Markov Chain Monte Carlo (MCMC) methods. The Bayes estimators have been obtained relative to both symmetric (squared error) and asymmetric (linex and general entropy) loss functions. Finally, to assess the performance of the proposed estimators, some numerical results using simulation study concerning different sample sizes are given.

KEYWORDS:  Generalized inverted Kumaraswamy distribution; progressive first-failure censored; loss functions; Lindley’s approximation

In this paper, we introduce a new four-parameter distribution called the new generalized Cauchy distribution (NGC). The structural properties of the new distribution are discussed. Expressions for the quantiles, mode, mean deviation, and distribution of order statistics are derived. It is shown that the distribution belongs to the class of subexponential distributions. NGC has regularly varying tails and is a member of the class of heavy-tailed distributions. It is shown that the tail weight of NGC is higher as compared to the Cauchy distribution. Parameters of NGC distribution are estimated by the percentile method, method of quantile least square, Cramer-Von Mises method, and method of maximum likelihood. Monte Carlo simulation is performed in order to investigate the performance of quantile least square estimates, Cramer-Von Mises estimates, and maximum likelihood estimates. The existence and uniqueness of maximum likelihood estimates are proved. The application of two real data sets shows the performance of the new model over other generalizations of Cauchy distribution.

KEYWORDS: Cramer-Von Mises method; Heavy tailed; Maximum likelihood estimation; Method of quantile least-square; Regular variation

Through this article, we investigate certain properties of an additive version of the log-inverse Weibull distribution including expressions for the cumulative distribution function, reliability function, hazard rate function, quantile function, raw moments, incomplete moments etc. Some structural properties of the distribution are considered along with the distribution and moments of its order statistics. The maximum likelihood estimation of its parameters and the elements of the Fisher information matrix are obtained. Further, the effciency of the distribution as a distributional model is illustrated using two real life datasets. Moreover, the asymptotic behaviour of the maximum likelihood estimators are examined with the help of simulated datasets.

KEYWORDS: Maximum likelihood estimation, Model selection, Moments, Order Statistics, Simulation

In this paper, we introduce and study type II generalized geometric Linnik (GeGL2) distribution. A representation of GeGL2 distribution is obatined. It is shown that GeGL2 distribution arises as the limit distribution of negative binomial sum of iid generalized Linnik random variables. GeGL2 stochastic process is introduced and studied.

KEYWORDS: Geometric gamma process, Geometric Linnik Distribution, Generalized Geometric Linnik Distribution, Linnik distribution, Stable Laws