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New Frontiers in Applied Mathematics and Statistics
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New Frontiers in Applied Mathematics and Statistics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Probability and Statistics".

Deadline for manuscript submissions: closed (31 December 2021) | Viewed by 17022

Special Issue Editor

Prof. Dr. Hari Mohan Srivastava

grade E-Mail Website
Guest Editor
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Interests: real and complex analysis; fractional calculus and its applications; integral equations and transforms; higher transcendental functions and their applications; q-series and q-polynomials; analytic number theory; analytic and geometric Inequalities; probability and statistics; inventory modeling and optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is intended to include selected peer-reviewed papers presented at the 2020 Asia-Pacific Conference on Applied Mathematics and Statistics, to be held on 17–19 February 2020 in Sydney, Australia. Other independent submissions dealing essentially with the theme of the conference (AMS 2020) will also be welcome. More details about the conference can be found at the following link:

http://www.apcams.org/.

There is a wide range of research topics, spanning both theoretical and systems research, for this Special Issue. We cordially invite researchers working in the field of applied mathematics and statistics to contribute original research papers or reviews to this Special Issue of MDPI’s SCIE-ranked journal, Mathematics.

Prof. Dr. H. M. Srivastava
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (7 papers)

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Research

8 pages, 309 KiB  
Article
A Note on Pareto-Type Distributions Parameterized by Its Mean and Precision Parameters
by Marcelo Bourguignon, Diego I. Gallardo and Héctor J. Gómez
Mathematics 2022, 10(3), 528; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030528 - 08 Feb 2022
Cited by 3 | Viewed by 2165
Abstract
Pareto-type distributions are well-known distributions used to fit heavy-tailed data. However, the standard parameterizations used for Pareto-type distributions are poorly suited to modeling. On this note, we suggest new parameterizations that are better suited to the purpose. In addition, we propose many regression [...] Read more.
Pareto-type distributions are well-known distributions used to fit heavy-tailed data. However, the standard parameterizations used for Pareto-type distributions are poorly suited to modeling. On this note, we suggest new parameterizations that are better suited to the purpose. In addition, we propose many regression models where the response variable is Pareto-type distributed using new parameterizations that are indexed by mean and precision parameters. The main motivation for these new parametrizations is the useful interpretation of the regression coefficients in terms of the mean and precision, as is usual in the context of regression models. The parameter estimation of these new models is performed, based on the maximum likelihood paradigm. Some numerical illustrations of the estimators are presented with a discussion of the obtained results. Finally, we illustrate the practicality of the new models by means of two applications to real data sets. Full article
(This article belongs to the Special Issue New Frontiers in Applied Mathematics and Statistics)
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16 pages, 300 KiB  
Article
Some Integral Inequalities in 𝒱-Fractional Calculus and Their Applications
by Hari Mohan Srivastava, Pshtiwan Othman Mohammed, Ohud Almutairi, Artion Kashuri and Y. S. Hamed
Mathematics 2022, 10(3), 344; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030344 - 24 Jan 2022
Cited by 2 | Viewed by 1962
Abstract
We consider the Steffensen–Hayashi inequality and remainder identity for V-fractional differentiable functions involving the six parameters truncated Mittag–Leffler function and the Gamma function. In view of these, we obtain some integral inequalities of Steffensen, Hermite–Hadamard, Chebyshev, Ostrowski, and Grüss type to the [...] Read more.
We consider the Steffensen–Hayashi inequality and remainder identity for V-fractional differentiable functions involving the six parameters truncated Mittag–Leffler function and the Gamma function. In view of these, we obtain some integral inequalities of Steffensen, Hermite–Hadamard, Chebyshev, Ostrowski, and Grüss type to the V-fractional calculus. Full article
(This article belongs to the Special Issue New Frontiers in Applied Mathematics and Statistics)
15 pages, 360 KiB  
Article
An Extended log-Lindley-G Family: Properties and Experiments in Repairable Data
by Ahmed M. T. Abd El-Bar, Willams B. F. da Silva and Abraão D. C. Nascimento
Mathematics 2021, 9(23), 3108; https://0-doi-org.brum.beds.ac.uk/10.3390/math9233108 - 02 Dec 2021
Cited by 3 | Viewed by 1313
Abstract
In this article, two new families of distributions are proposed: the generalized log-Lindley-G (GLL-G) and its counterpart, the GLL*-G. These families can be justified by their relation to the log-Lindley model, an important assumption for describing social and economic phenomena. Specific GLL models [...] Read more.
In this article, two new families of distributions are proposed: the generalized log-Lindley-G (GLL-G) and its counterpart, the GLL*-G. These families can be justified by their relation to the log-Lindley model, an important assumption for describing social and economic phenomena. Specific GLL models are introduced and studied. We show that the GLL density is rewritten as a two-member linear combination of the exponentiated G-densities and that, consequently, many of its mathematical properties arise directly, such as moment-based expressions. A maximum likelihood estimation procedure for the GLL parameters is provided and the behavior of the resulting estimates is evaluated by Monte Carlo experiments. An application to repairable data is made. The results argue for the use of the exponential law as the basis for the GLL-G family. Full article
(This article belongs to the Special Issue New Frontiers in Applied Mathematics and Statistics)
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14 pages, 881 KiB  
Article
A Comparative Study of the Fractional-Order Clock Chemical Model
by Hari Mohan Srivastava and Khaled M. Saad
Mathematics 2020, 8(9), 1436; https://0-doi-org.brum.beds.ac.uk/10.3390/math8091436 - 27 Aug 2020
Cited by 28 | Viewed by 2196
Abstract
In this paper, a comparative study has been made between different algorithms to find the numerical solutions of the fractional-order clock chemical model (FOCCM). The spectral collocation method (SCM) with the shifted Legendre polynomials, the two-stage fractional Runge–Kutta method (TSFRK) and the four-stage [...] Read more.
In this paper, a comparative study has been made between different algorithms to find the numerical solutions of the fractional-order clock chemical model (FOCCM). The spectral collocation method (SCM) with the shifted Legendre polynomials, the two-stage fractional Runge–Kutta method (TSFRK) and the four-stage fractional Runge–Kutta method (FSFRK) are used to approximate the numerical solutions of FOCCM. Our results are compared with the results obtained for the numerical solutions that are based upon the fundamental theorem of fractional calculus as well as the Lagrange polynomial interpolation (LPI). Firstly, the accuracy of the results is checked by computing the absolute error between the numerical solutions by using SCM, TSFRK, FSFRK, and LPI and the exact solution in the case of the fractional-order logistic equation (FOLE). The numerical results demonstrate the accuracy of the proposed method. It is observed that the FSFRK is better than those by SCM, TSFRK and LPI in the case of an integer order. However, the non-integer orders in the cases of the SCM and LPI are better than those obtained by using the TSFRK and FSFRK. Secondly, the absolute error between the numerical solutions of FOCCM based upon SCM, TSFFRK, FSFRK, and LPI for integer order and non-integer order has been computed. The absolute error in the case of the integer order by using the three methods of the third order is considered. For the non-integer order, the order of the absolute error in the case of SCM is found to be the best. Finally, these results are graphically illustrated by means of different figures. Full article
(This article belongs to the Special Issue New Frontiers in Applied Mathematics and Statistics)
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15 pages, 331 KiB  
Article
Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain
by Bilal Khan, Hari M. Srivastava, Nazar Khan, Maslina Darus, Muhammad Tahir and Qazi Zahoor Ahmad
Mathematics 2020, 8(8), 1334; https://0-doi-org.brum.beds.ac.uk/10.3390/math8081334 - 11 Aug 2020
Cited by 29 | Viewed by 2509
Abstract
First, by making use of the concept of basic (or q-) calculus, as well as the principle of subordination between analytic functions, generalization Rq(h) of the class R(h) of analytic functions, which are associated with [...] Read more.
First, by making use of the concept of basic (or q-) calculus, as well as the principle of subordination between analytic functions, generalization Rq(h) of the class R(h) of analytic functions, which are associated with the leaf-like domain in the open unit disk U, is given. Then, the coefficient estimates, the Fekete–Szegö problem, and the second-order Hankel determinant H2(1) for functions belonging to this class Rq(h) are investigated. Furthermore, similar results are examined and presented for the functions zf(z) and f−1(z). For the validity of our results, relevant connections with those in earlier works are also pointed out. Full article
(This article belongs to the Special Issue New Frontiers in Applied Mathematics and Statistics)
11 pages, 787 KiB  
Article
Statistical Deferred Nörlund Summability and Korovkin-Type Approximation Theorem
by Hari Mohan Srivastava, Bidu Bhusan Jena and Susanta Kumar Paikray
Mathematics 2020, 8(4), 636; https://0-doi-org.brum.beds.ac.uk/10.3390/math8040636 - 21 Apr 2020
Cited by 28 | Viewed by 2542
Abstract
The concept of the deferred Nörlund equi-statistical convergence was introduced and studied by Srivastava et al. [Rev. Real Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. (RACSAM) 112 (2018), 1487–1501]. In the present paper, we have studied the notion of the deferred Nörlund [...] Read more.
The concept of the deferred Nörlund equi-statistical convergence was introduced and studied by Srivastava et al. [Rev. Real Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. (RACSAM) 112 (2018), 1487–1501]. In the present paper, we have studied the notion of the deferred Nörlund statistical convergence and the statistical deferred Nörlund summability for sequences of real numbers defined over a Banach space. We have also established a theorem presenting a connection between these two interesting notions. Moreover, based upon our proposed methods, we have proved a new Korovkin-type approximation theorem with algebraic test functions for a sequence of real numbers on a Banach space and demonstrated that our theorem effectively extends and improves most of the earlier existing results (in classical and statistical versions). Finally, we have presented an example involving the generalized Meyer–König and Zeller operators of a real sequence demonstrating that our theorem is a stronger approach than its classical and statistical versions. Full article
(This article belongs to the Special Issue New Frontiers in Applied Mathematics and Statistics)
16 pages, 311 KiB  
Article
Some Janowski Type Harmonic q-Starlike Functions Associated with Symmetrical Points
by Muhammad Arif, Omar Barkub, Hari Mohan Srivastava, Saleem Abdullah and Sher Afzal Khan
Mathematics 2020, 8(4), 629; https://0-doi-org.brum.beds.ac.uk/10.3390/math8040629 - 19 Apr 2020
Cited by 39 | Viewed by 2594
Abstract
The motive behind this article is to apply the notions of q-derivative by introducing some new families of harmonic functions associated with the symmetric circular region. We develop a new criterion for sense preserving and hence the univalency in terms of q [...] Read more.
The motive behind this article is to apply the notions of q-derivative by introducing some new families of harmonic functions associated with the symmetric circular region. We develop a new criterion for sense preserving and hence the univalency in terms of q-differential operator. The necessary and sufficient conditions are established for univalency for this newly defined class. We also discuss some other interesting properties such as distortion limits, convolution preserving, and convexity conditions. Further, by using sufficient inequality, we establish sharp bounds of the real parts of the ratios of harmonic functions to its sequences of partial sums. Some known consequences of the main results are also obtained by varying the parameters. Full article
(This article belongs to the Special Issue New Frontiers in Applied Mathematics and Statistics)
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