Modeling the Choice of the Innovation and Investment Strategy for the Implementation of Modernization Potential

Since modernization challenges of microeconomic systems are implemented through strategic management of the modernization potential development of enterprises, the rationale for choosing an exclusive innovation and investment strategy is proposed. An algorithm for making managerial decisions based on the model of "preferences in the implementation of investment and innovation strategies" ("PIIIS") is built. The model is based on the concept of strategic management, economic and mathematical hierarchy of potential levels of cognitive judgment, optimization of resources on demand and the structure of innovation and investment strategies. This allows to ensure the efficiency and resource conservation of individual innovation and investment strategies in modernization potential of the enterprise. The sequence of establishing preferences of innovation and investment strategies for activating modernization potential of microeconomic systems is proposed. To model the process of granting preferences to innovation and investment strategies, a system of coefficients based on the potential profile level using cognitive judgments is substantiated. Resource-providing, accumulating, implementation and resulting levels of the modernization potential development are singled out. According to the profile levers, target tasks and alternatives of preferences of innovation and investment strategies for the modernization potential development are identified. Decomposition of tasks of granting preferences to innovation and investment strategies to intensify modernization potential of microeconomic systems is substantiated. It is proposed to use mathematical tools for the analysis of hierarchies, based on mathematical and cognitive judgments based on the T. Saaty model. Application of the Pareto model for the distribution of the coefficients influence in the effectiveness of the components analysis of the potential profile is presented. The choice of innovation and investment strategies for the modernization potential development for enterprises in the infrastructure sector of Ukraine is analyzed and determined.

Best Prediction Method for Progressive Type-II Censored Samples under New Pareto Model with Applications

This paper describes two prediction methods for predicting the non-observed (censored) units under progressive Type-II censored samples. The lifetimes under consideration are following a new two-parameter Pareto distribution. Furthermore, point and interval estimation of the unknown parameters of the new Pareto model is obtained. Maximum likelihood and Bayesian estimation methods are considered for that purpose. Since Bayes estimators cannot be expressed explicitly, Gibbs and the Markov Chain Monte Carlo techniques are utilized for Bayesian calculation. We use the posterior predictive density of the non-observed units to construct predictive intervals. A simulation study is performed to evaluate the performance of the estimators via mean square errors and biases and to obtain the best prediction method for the censored observation under progressive Type-II censoring scheme for different sample sizes and different censoring schemes.

Pareto Distribution under Hybrid Censoring: Some Estimation

In the present study, the Pareto model is considered as the model from which observations are to be estimated using a Bayesian approach. Properties of the Bayes estimators for the unknown parameters have studied by using different asymmetric loss functions on hybrid censoring pattern and their risks have compared. The properties of maximum likelihood estimation and approximate confidence length have also been investigated under hybrid censoring. The performances of the procedures are illustrated based on simulated data obtained under the Metropolis-Hastings algorithm and a real data set.

Generalized Inference on Stress-Strength Reliability in Generalized Pareto Model

The article focuses on the inference of stress-strength reliability in generalized Pareto model using the generalized variable approach and bootstrap percentile method. Simulation studies are conducted to obtain expected lengths and coverage probabilities of confidence intervals constructed using the generalized variable and the bootstrap percentile methods. An example consisting of real stress-strength data is also presented for illustrative purposes.

The application of the Pareto distribution to approximate income distributions of wealthy households in Poland

The aim of the paper is to approximate the equivalent income distributions of wealthy households in particular socio-economic groups using the Pareto distribution, with parameters estimated by means of the maximum likelihood estimation method. Households whose income exceeded the established wealth threshold were classified as wealthy households. Income distributions of wealthy households are usually non-modal and heavy-tailed, thus, the Pareto distribution was applied as their theoretical model. The equivalent income of wealthy households in Poland was analysed in total and in particular socio-economic groups. The research was based on data from the 2014–2017 Household Budget Survey. Selected similarity measures were used to examine the degree to which the theoretical distributions proved consistent with the empirical ones. The obtained results confirmed the high level of consistency of empirical income distributions with the Pareto model. Moreover, very good approximations were obtained especially for wealthy households of employees and self-employed, as well as pensioners. Slightly worse results were obtained for the farmers group. Theoretical distributions well fitted to empirical data were used to estimate selected distribution characteristics, including measures of location, dispersion and inequality, and to compare the different groups in terms of their wealth.

The Bayesian Inference of Pareto Models Based on Information Geometry

Bayesian methods have been rapidly developed due to the important role of explicable causality in practical problems. We develope geometric approaches to Bayesian inference of Pareto models, and give an application to the analysis of sea clutter. For Pareto two-parameter model, we show the non-existence of α-parallel prior in general, hence we adopt Jeffreys prior to deal with the Bayesian inference. Considering geodesic distance as the loss function, an estimation in the sense of minimal mean geodesic distance is obtained. Meanwhile, by involving Al-Bayyati’s loss function we gain a new class of Bayesian estimations. In the simulation, for sea clutter, we adopt Pareto model to acquire various types of parameter estimations and the posterior prediction results. Simulation results show the advantages of the Bayesian estimations proposed and the posterior prediction.

Estimation of Beta-Pareto Distribution Based on Several Optimization Methods

This paper is concerned with the maximum likelihood estimators of the Beta-Pareto distribution introduced in Akinsete et al. (2008), which comes from the mixing of two probability distributions, Beta and Pareto. Since these estimators cannot be obtained explicitly, we use nonlinear optimization methods that numerically provide these estimators. The methods we investigate are the method of Newton-Raphson, the gradient method and the conjugate gradient method. Note that for the conjugate gradient method we use the model of Fletcher-Reeves. The corresponding algorithms are developed and the performances of the methods used are confirmed by an important simulation study. In order to compare between several concurrent models, namely generalized Beta-Pareto, Beta, Pareto, Gamma and Beta-Pareto, model criteria selection are used. We firstly consider completely observed data and, secondly, the observations are assumed to be right censored and we derive the same type of results.