In this article we consider the Stochastic restricted ridge estimation in semi-parametric linear models when the covariates are measured with additive errors. The development of penalized corrected likelihood method in such model is the basis for derivation of ridge estimates. The asymptotic normality of the resulting estimates are established. Also, necessary and sufficient conditions, for the superiority of the pro-posed estimator over its counterpart, for selecting the ridge parameter k are obtained. A Monte Carlo simulation study is also performed to illustrate the finite sample perfor-mance of the proposed procedures. Finally theoretical results are applied to Egyptian pottery Industry data set.

In this study, the Stochastic restricted and unrestricted two-parameter estimators of fixed and random effects are investigated in the linear mixed measurement error models. For this purpose, the asymptotic properties and then the comparisons under the criterion of mean squared error matrix (MSEM) are derived. Furthermore, the proposed methods are used for estimating the biasing parameters. Finally, a real data analysis and a simulation study are provided to evaluate the performance of the proposed estimators.

In this paper, we introduce the weighted ridge estimators of fixed and random effects in Stochastic restricted linear mixed measurement error models when collinearity is present. The asymptotic properties of the resulting estimates are examined. The necessary and sufficient conditions, for the superiority of the weighted ridge estimators against the weighted estimator in order to select the ridge parameter based on the mean squared error matrix of estimators, are investigated. Finally, theoretical results are augmented with a simulation study and a numerical example.

Efficiency in agricultural production is indicative of the efficiency level of farm households in their farming activities. Farmers in developing countries do not make use of all the potential technological resources, thus making inefficient decisions in their agricultural activities. Herein, technical efficiency in relation with the production of three types of rice crop (Boro, Aus and Aman) was evaluated, with some determinants of technical efficiency identified, in Bangladesh. It was attempted, throughout this study, to access the status of technical efficiency in rice production in Bangladesh for panel data while using the Stochastic Frontier Production Model with either of truncated normal or half-normal distributional assumptions. Both time-variant and time-invariant inefficiency effects models were estimated, one at a time. Collected data from agricultural sector pertaining to three main rice crops in Bangladesh for the period of 1980 to 2008 were made used of throughout the study. The results revealed that technical efficiency gradually increased over the reference period with the half normal distribution being found preferable to the truncated normal distribution as regards the technical inefficiency effects. The value of technical efficiency was found high for Boro rice while low for Aus in comparison with Aman rice in Bangladesh for both distributions in either of time-variant or invariant ones. It was observed that the most efficient rice production system has occurred for the case of Boro with a technical efficiency of 0.98. Year wise mean technical efficiency increased during the reference time periods.

Soft set theory has been well-known as an innovative approach to managing uncertainty-related problems and modelling uncertainty since Molodtsov introduced it in 1999. It has been applied in a variety of contexts, both theoretical and practical. The core concept of the theory, soft set operations, has piqued the curiosity of researchers ever since it was developed. A number of restricted and extended soft set operations have been defined, and their characteristics have been investigated. In this study, we present a new restricted and extended soft set operation, which we refer to as extended gamma and restricted gamma operation, and we study their fundamental algebraic properties in detail. Additionally, this operation's distributions over other soft-set operations are examined. Considering the algebraic properties of the extended gamma operation and its distribution rules, we show that when combined with other types of soft sets, it forms several important algebraic structures, like semirings and near-semirings, in the collection of soft sets over the universe. This theoretical study is highly significant from both a theoretical and practical standpoint, as the main notion of the theory is the operations of soft sets, which provide the basis for many applications, such as cryptology and optimal decision-making procedures.

We study two foremost Mahonian statistics, the major index and the inversion number for a class of binary words called restricted Fibonacci words. The language of restricted Fibonacci words satisfies recurrences which allow for the calculation of the generating functions in two different ways. These yield identities involving the $q$-binomial coefficients and provide non-standard $q$-analogues of the Fibonacci numbers. The major index generating function for restricted Fibonacci words turns out to be a $q$-power multiple of the inversion generating function.

Finding the location for plans like factories or warehouses for any organization is an important and strategic decision. Costs of transportation which are the main part of the price of the goods, is the function of the location of these projects. to find the optimum location of these projects, there have been various methods proposed which are usually defined (not random). In reality and in dealing with real world conditions, taking into account influential and effective parameters leads to unexpected results. In this research, while introducing these defined algorithms, it been tried to random location model based on the existing models. Regarding this, by studying the models taken in random location we tried to propose an efficient and effective model. For this purpose, by using randomized planning and randomized constrained planning, we turn random model to defined model, which is solvable by using the last algorithm or standard planning methods.