Aladdin Shamilov

On the Identifiability of Finite Mixtures Based on the Union of Logarithmic Series and Discrete Rectangular Families

In this paper, finite mixtures of the union of Logarithmic Series and Discrete Rectangular families are proved to be identifiable. The sufficient condition for the identifiability of finite mixtures given by Atienza et al. (Metrika 63:215–221, 2006) is applied instead of mostly used Teicher’s condition (Teicher, Ann Math Stat 34: 1265–1269, 1963). The choice of distribution is made in order to stress the fact that, contrarily to Teicher’s approach, Atienza et al.’s theorem being used does apply to heterogeneous parametric families.

Statistical Model Development for Military Aircraft Engine Exhaust Emissions Data

Statistical regression models have a wide usage in various estimation problems. They can be used to find a relationship between dependent and independent variables. Generally, it is using regression parametric models to find the type of relationship between variables. But some problems could not be estimated with linear models, as they have a nonlinear effect on dependent variable. This study aims to show the difference between linear and nonlinear techniques. In this study, emission parameters of a military-type turboprop engine is determined at unmeasured operating points on the basis of data collected at various loads with the aid of regression techniques. It is using multivariate linear regression, additive models with B-spline basis function, and smoothing splines. Three different techniques used to reveal best approximation to the dataset. It is observed that the effect of three parameters: revolution per minute (min-1), air/fuel ratio (kg air/kg fuel), and mass flow rate (kg.s-1) to different mass flow rates (CO (kg/s), CO2 (kg/s); UHC (kg/s), NO2 (kg/s)). In the end of the study, results obtained from benefited approximations were compared with each other using MSE (mean squared error) performance criteria.

On developed estimation methods via unique and multiple parametrization

In the present study, two methods, based on entropy optimization principle, to estimate missing (or forecasting) values in the given time series are suggested. In the first method successively replaces the missing values with the parameter value minimizing entropy of multivariate normal distribution representing MaxEnt approximation of the time series which arises by parameterization with a single parameter. In the second method, all missing values are parameterized with multiple parameters for each missing value and are estimated at a time. These methods are applied to biomedical data, missing values of which estimated via Kalman, and comparisons are given. These processes are realized by programs written in MATLAB.