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Asian Journal of Mathematics & Statistics
eISSN: 2077-2068
pISSN: 1994-5418

Editor-in-Chief:  Haroon Mohamad Barakat
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Research Article
A New Approach to Randomized Response Model Using Fuzzy Numbers
Tanveer Ahmad Tarray, Peer Bilal and Muzafar Rasool
The crux of this study is to consider a randomized response model using allocation problem in presence of non-response based on model and minimize the variance subject to cost constraint. The costs (measurement costs and total budget of the survey) in the cost constraint are assumed as fuzzy numbers, in particular triangular and trapezoidal fuzzy numbers due to the ease of use. The problem formulated is solved by using Lagrange multipliers technique and the optimum allocation obtained in the form of fuzzy numbers is converted into crisp form using α-cut method at a prescribed value of α. Numerical illustrations are also given in support of the present study and the results are formulated through LINGO.
Research Article
Basic Analogue of Double Sumudu Transform and its Applicability in Population Dynamics
Javid Ahmad Ganie, Altaf Ahmad and Renu Jain
In this study basic analogue of double Sumudu transform of functions expressible as polynomials or convergent series are derived. The applicability of this relatively new transform is demonstrated using some special functions, which arise in the solution of evolution equations of population dynamics as well as partial differential equations.
Research Article
Matrix Representation of an All-inclusive Fibonacci Sequence
Tanveer Ahmad Tarray, Parvaiz Ahmad Naik and Riyaz Ahmad Najar
Background and Objectives: Fibonacci sequence is a sequence of positive integers that has been studied over several years. The aim of this paper was to suggest new generalized Fibonacci sequence to a particular class of recursive sequence. Materials and Methods: The equilibrium point of the model was investigated and a new sequence. The matrix method was applied to perform the generalization. Results: The nth power of the generating matrix for this generalized Fibonacci sequence was established and some basic properties of this sequence were obtained by matrix methods. Conclusion: Cassini’s identity and Binet’s formula for the generalized Fibonacci sequence was obtained.
Research Article
Population Mean Estimation Using Ratio-cum Product Compromised-method of Imputation in Two-phase Sampling Scheme
Krishnajyothi Nath and B.K. Singh
Background and Objective: In literature there has been a study on ratio cum product estimator of a finite population mean in two-phase sampling in sample surveys, but it lacks study when there is non-response on sample observations. So the main objective of this paper was to propose three generalized classes of ratio cum product compromised imputation techniques in presence of missing values in two-phase sampling design and its properties have been studied. Materials and Methods: The estimators were compared with other existing estimators in two different designs. The bias and M.S.E. of suggested estimators were derived in the form of population parameters using the concept of large sample approximations. Results: The results showed the superiority of the proposed estimators over the existing methods. Numerical studies are performed over two population data sets using the expressions of bias and M.S.E. and their efficiencies are compared with other existing estimators. Conclusion: It was observed that the proposed estimators were performing better than the estimators taken for comparisons in the presence of missing data.
Research Article
Generating q-Analogue of I-Function Satisfying Truesdell's Ascending Fq-Equation
Altaf Ahmad Bhat, Renu Jain and Deepak Kumar Jain
Various forms of q-analogue of I-function satisfying Truesdell’s descending Fq-equation have been studied and various generating functions by the application of these various forms have been derived. The aim of this study was to produce q-analogue of I-function which fulfilling Truesdell’s Ascending Fq-equation. In this study, various forms of q-analogue of I-function satisfying Truesdell’s ascending Fq-equation have been obtained. Certain generating functions for q-analogue of I-function have been derived by using these forms. Further, some particular cases of these results in terms of q-analogue of H-and G-functions which appear to be new have also been obtained.

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