Gupta et al (2002) suggested an optional randomized response model under the assumption that the mean of the scrambling variable S is ‘unity’ [i.e. µs = 1]. This assumption limits the use of Gupta et al’s (2002) randomized response model. Keeping this in view we have suggested a modified optional randomized response model which can be used in practice without any supposition and restriction over the mean (µs) of the scrambling variables S. It has been shown that the estimator of the mean of the stigmatized variable based on the proposed optional randomized response sampling is more efficient than the Eicchorn and Hayre (1983) procedure and Gupta et al’s (2002) optional randomized technique when the mean of the scrambling S is larger than unity [i.e. µs > 1]. A numerical illustration is given in support of the present study.
In this paper, an effectual and new modification in Laplace Adomian decomposition method based on Bernstein polynomials is proposed to find the solution of nonlinear Volterra integral and integro-differential equations. The performance and capability of the proposed idea is endorsed by comparing the exact and approximate solutions for three different examples on Volterra integral, integro-differential equations of the first and second kinds. The results shown through tables and figures demonstrate the accuracy of our method. It is concluded here that the non orthogonal polynomials can also be used for Laplace Adomian decomposition method. In addition, convergence analysis of the modified technique is also presented.
Fisher information is of key importance in estimation theory. It is used as a tool for characterizing complex signals or systems, with applications, e.g. in biology, geophysics and signal processing. The problem of minimizing Fisher information in a set of distributions has been studied by many researchers. In this paper, based on some rather simple statistical reasoning, we provide an alternative proof for the fact that Gaussian distribution with finite variance minimizes the Fisher information over all distributions with the same variance.
Adil Rashid, Tariq Rashid Jan, Akhtar Hussain Bhat and Z. Ahmad
There are diverse lifetime models available to the researchers to predict the uncertain behavior of random events but at times they fail to provide adequate fit for some complex and new data sets. New probability distributions are emerging as lifetime models to meet this ever growing demand of modeling complex real world phenomena from different sciences with better efficiency. Here, in this manuscript we shall compose Ailamujia distribution with that of power series distribution. This newly developed distribution called Ailamujia power series distribution reduces to four new special lifetime models on simple specific function parametric setting. Apart from this some important mathematical properties in the form of propositions will also be discussed. Furthermore, characterization and some statistical properties that include mgf, moments, and parameter estimation have also been discussed. Finally, the potency of newly proposed model has been analyzed statistically and graphically and it has been established from the statistical analysis that newly proposed model offers a better fit when it comes to model some lifetime data set.
In the present paper, we introduce and investigate two new subclasses QΣ(n; y;k) and BΣ(n;β;k) of bi-valent functions in the unit disk U. For functions belonging to the classes QΣ(n;y;k) and BΣ(n;β;k), we obtain estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3|.
In this article, we introduce some examples of cubic rank transmuted distributions proposed by Granzatto et al. (2017). The statistical aspects of the introduced distributions such as probability density functions, hazard rate functions and reliability functions are studied. The maximum likelihood estimation method is used in order to estimate the parameters of interest. Finally, real data examples are applied for the illustration of these distributions.
Elliptic-type integral plays a major role in the study of different problems of physics and technology including fracture mechanics. Many papers have been written for various families of elliptic-type integrals. Due to their applications here, we are presenting an organized study of certain generalized family of incomplete elliptic integral. The obtained results are basic in nature have various generalizations. While using the fractional integral operator of Riemann-Liouville type, we found several obvious hyper geometric representations. Which are further used to originate many definite integrals relating to their modules and amplitude of elliptic type generalized incomplete integrals.
Accurate and reliable air passenger demand is very important for policy-making and planning by tourism management as well as by airline authorities. Therefore, this article proposed a novel hybrid method based on rough set theory (RST) to construct decision rules for long-term forecasting of air passengers. Level (mean) and trend components are first estimated from the air passengers time series data using DES model in the formulation of the proposed hybrid method. Then the rough set theory is employed to combine the output of DES model and generated decision rules is used to forecasting air passengers. We compare the proposed approach with other time series models using a corrected classified accuracy (CCA) criterion. For the empirical analysis, yearly air transport passenger from 1992 to 2004 is used. Empirical results show that the proposed method is highly accurate with the higher corrected classified accuracy. Also, forecasting accuracy of the proposed method is better than the other time series approaches.