Mathematics and Statistics Faculty and Staff PublicationsCopyright (c) 2020 University of New Mexico All rights reserved.
https://digitalrepository.unm.edu/math_fsp
Recent documents in Mathematics and Statistics Faculty and Staff Publicationsen-usFri, 27 Mar 2020 12:27:37 PDT3600RANDOMNESS AND OPTIMAL ESTIMATION IN DATA SAMPLING
https://digitalrepository.unm.edu/math_fsp/194
https://digitalrepository.unm.edu/math_fsp/194Mon, 24 Feb 2020 08:17:01 PST
The purpose of this book is to postulate some theories and test them numerically. Estimation is often a difficult task and it has wide application in social sciences and financial market. In order to obtain the optimum efficiency for some classes of estimators, we have devoted this book into three specialized sections: Part 1. In this section we have studied a class of shrinkage estimators for shape parameter beta in failure censored samples from two-parameter Weibull distribution when some 'apriori' or guessed interval containing the parameter beta is available in addition to sample information and analyses their properties. Some estimators are generated from the proposed class and compared with the minimum mean squared error (MMSE) estimator. Numerical computations in terms of percent relative efficiency and absolute relative bias indicate that certain of these estimators substantially improve the MMSE estimator in some guessed interval of the parameter space of beta, especially for censored samples with small sizes. Subsequently, a modified class of shrinkage estimators is proposed with its properties. Part2. In this section we have analyzed the two classes of estimators for population median MY of the study character Y using information on two auxiliary characters X and Z in double sampling. In this section we have shown that the suggested classes of estimators are more efficient than the one suggested by Singh et al (2001). Estimators based on estimated optimum values have been also considered with their properties. The optimum values of the first phase and second phase sample sizes are also obtained for the fixed cost of survey.
]]>
Florentin Smarandache et al.SAMPLING STRATEGIES FOR FINITE POPULATION USING AUXILIARY INFORMATION
https://digitalrepository.unm.edu/math_fsp/193
https://digitalrepository.unm.edu/math_fsp/193Mon, 24 Feb 2020 08:16:58 PST
The present book aims to present some improved estimators using auxiliary and attribute information in case of simple random sampling and stratified random sampling and in some cases when non-response is present. This volume is a collection of five papers, written by seven co-authors (listed in the order of the papers): Sachin Malik, Rajesh Singh, Florentin Smarandache, B. B. Khare, P. S. Jha, Usha Srivastava and Habib Ur. Rehman. The first and the second papers deal with the problem of estimating the finite population mean when some information on two auxiliary attributes are available. In the third paper, problems related to estimation of ratio and product of two population mean using auxiliary characters with special reference to non-response are discussed. In the fourth paper, the use of coefficient of variation and shape parameters in each stratum, the problem of estimation of population mean has been considered. In the fifth paper, a study of improved chain ratio-cum-regression type estimator for population mean in the presence of non-response for fixed cost and specified precision has been made. The authors hope that the book will be helpful for the researchers and students that are working in the field of sampling techniques.
]]>
Florentin Smarandache et al.STUDIES IN STATISTICAL INFERENCE, SAMPLING TECHNIQUES AND DEMOGRAPHY
https://digitalrepository.unm.edu/math_fsp/192
https://digitalrepository.unm.edu/math_fsp/192Mon, 24 Feb 2020 08:16:55 PST
This volume is a collection of five papers. Two chapters deal with problems in statistical inference, two with inferences in finite population, and one deals with demographic problem. The ideas included here will be useful for researchers doing works in these fields. The following problems have been discussed in the book: Chapter 1. In this chapter optimum statistical test procedure is discussed. The test procedures are optimum in the sense that they minimize the sum of the two error probabilities as compared to any other test. Several examples are included to illustrate the theory. Chapter 2. In testing of hypothesis situation if the null hypothesis is rejected will it automatically imply alternative hypothesis will be accepted? This problem has been discussed by taking examples from normal distribution. Chapter 3. In this section improved chain-ratio type estimator for estimating population mean using some known values of population parameter(s) has been discussed. The proposed estimators have been compared with two-phase ratio estimator and some other chain ratio type estimators. Chapter 4. In this section we have analysed exponential ratio and exponential product type estimators using two auxiliary variables are proposed for estimating unknown population variance 2 yS . Problem is extended to the case of two-phase sampling. Chapter 5. In this section structural dynamics of various causes of migration in Jaipur was analysed. Reasons of migration from rural to urban areas and that of males and females are studied.
]]>
Florentin Smarandache et al.USES OF SAMPLING TECHNIQUES & INVENTORY CONTROL WITH CAPACITY CONSTRAINTS
https://digitalrepository.unm.edu/math_fsp/191
https://digitalrepository.unm.edu/math_fsp/191Mon, 24 Feb 2020 08:16:52 PST
The main aim of the present book is to suggest some improved estimators using auxiliary and attribute information in case of simple random sampling and stratified random sampling and some inventory models related to capacity constraints. This volume is a collection of five papers, written by six co-authors (listed in the order of the papers): Dr. Rajesh Singh, Dr. Sachin Malik, Dr. Florentin Smarandache, Dr. Neeraj Kumar, Mr. Sanjey Kumar & Pallavi Agarwal. In the first chapter authors suggest an estimator using two auxiliary variables in stratified random sampling for estimating population mean. In second chapter they proposed a family of estimators for estimating population means using known value of some population parameters. In Chapter third an almost unbiased estimator using known value of some population parameter(s) with known population proportion of an auxiliary variable has been used. In Chapter four the authors investigates a fuzzy economic order quantity model for two storage facility. The demand, holding cost, ordering cost, storage capacity of the own - warehouse are taken as trapezoidal fuzzy numbers. And in Chapter five a two-warehouse inventory model deals with deteriorating items, with stock dependent demand rate and model affected by inflation under the pattern of time value of money over a finite planning horizon. Shortages are allowed and partially backordered depending on the waiting time for the next replenishment. The purpose of this model is to minimize the total inventory cost by using the genetic algorithm. This book will be helpful for the researchers and students who are working in the field of sampling techniques and inventory control.
]]>
Florentin Smarandache et al.Advances of Standard and Nonstandard Neutrosophic Theories
https://digitalrepository.unm.edu/math_fsp/190
https://digitalrepository.unm.edu/math_fsp/190Mon, 24 Feb 2020 08:16:48 PST
In this book, we approach different topics related to neutrosophics, such as: Neutrosophic Set, Intuitionistic Fuzzy Set, Inconsistent Intuitionistic Fuzzy Set, Picture Fuzzy Set, Ternary Fuzzy Set, Pythagorean Fuzzy Set, Atanassov’s Intuitionistic Fuzzy Set of second type, Spherical Fuzzy Set, n-HyperSpherical Neutrosophic Set, q-Rung Orthopair Fuzzy Set, truth-membership, indeterminacy-membership, falsehood-nonmembership, Regret Theory, Grey System Theory, ThreeWays Decision, n-Ways Decision, Neutrosophy, Neutrosophication, Neutrosophic Probability, Refined Neutrosophy, Refined Neutrosophication, Nonstandard Analysis; Extended Nonstandard Analysis; Open and Closed Monads to the Left/Right; Pierced and Unpierced Binads; MoBiNad Set; infinitesimals; infinities; nonstandard reals; standard reals; Nonstandard Neutrosophic Lattices of First Type (as poset) and Second Type (as algebraic structure); Nonstandard Neutrosophic Logic; Extended Nonstandard Neutrosophic Logic; Nonstandard Arithmetic Operations; Nonstandard Unit Interval; Nonstandard Neutrosophic Infimum; Nonstandard Neutrosophic Supremum, Plithogeny; Plithogenic Set; Neutrosophic Set; Plithogenic Operators, Neutrosophic Triplets, (Axiom, NeutroAxiom, AntiAxiom), (Law, NeutroLaw, AntiLaw), (Associativity, NeutroAssociaticity, AntiAssociativity), (Commutativity, NeutroCommutativity, AntiCommutativity), (WellDefined, NeutroDefined, AntiDefined), (Semigroup, NeutroSemigroup, AntiSemigroup), (Group, NeutroGroup, AntiGroup), (Ring, NeutroRing, AntiRing), (Algebraic Structures, NeutroAlgebraic Structures, AntiAlgebraic Structures), (Structure, NeutroStructure, AntiStructure), (Theory, NeutroTheory, AntiTheory), Sdenying an Axiom, Multispace with Multistructure, and so on.
]]>
Florentin SmarandacheIntroduction to NeutroAlgebraic Structures and AntiAlgebraic Structures (revisited)
https://digitalrepository.unm.edu/math_fsp/189
https://digitalrepository.unm.edu/math_fsp/189Mon, 24 Feb 2020 08:16:45 PST
In all classical algebraic structures, the Laws of Compositions on a given set are well-defined. But this is a restrictive case, because there are many more situations in science and in any domain of knowledge when a law of composition defined on a set may be only partially-defined (or partially true) and partially-undefined (or partially false), that we call NeutroDefined, or totally undefined (totally false) that we call AntiDefined. Again, in all classical algebraic structures, the Axioms (Associativity, Commutativity, etc.) defined on a set are totally true, but it is again a restrictive case, because similarly there are numerous situations in science and in any domain of knowledge when an Axiom defined on a set may be only partially-true (and partially-false), that we call NeutroAxiom, or totally false that we call AntiAxiom. Therefore, we open for the first time in 2019 new fields of research called NeutroStructures and AntiStructures respectively.
]]>
Florentin SmarandacheAUXILIARY INFORMATION AND A PRIORI VALUES IN CONSTRUCTION OF IMPROVED ESTIMATORS
https://digitalrepository.unm.edu/math_fsp/188
https://digitalrepository.unm.edu/math_fsp/188Mon, 03 Feb 2020 08:18:28 PST
This volume is a collection of six papers on the use of auxiliary information and a priori values in construction of improved estimators. The work included here will be of immense application for researchers and students who employ auxiliary information in any form. Below we discuss each paper: 1. Ratio estimators in simple random sampling using information on auxiliary attribute. Prior knowledge about population mean along with coefficient of variation of the population of an auxiliary variable is known to be very useful particularly when the ratio, product and regression estimators are used for estimation of population mean of a variable of interest. However, the fact that the known population proportion of an attribute also provides similar type of information has not drawn as much attention. In fact, such prior knowledge can also be very useful when a relation between the presence (or absence) of an attribute and the value of a variable, known as point biserial correlation, is observed. Taking into consideration the point biserial correlation between a variable and an attribute, Naik and Gupta (1996) defined ratio, product and regression estimators of population mean when the prior information of population proportion of units, possessing the same attribute is available. In the present paper, some ratio estimators for estimating the population mean of the variable under study, which make use of information regarding the population proportion possessing certain attribute are proposed. The expressions of bias and mean squared error (MSE) have been obtained. The results obtained have been illustrated numerically by taking some empirical populations considered in the literature.
]]>
Florentin Smarandache et al.Computational Modeling in Applied Problems: collected papers on econometrics, operations research, game theory and simulation
https://digitalrepository.unm.edu/math_fsp/187
https://digitalrepository.unm.edu/math_fsp/187Mon, 03 Feb 2020 08:18:24 PST
Computational models pervade all branches of the exact sciences and have in recent times also started to prove to be of immense utility in some of the traditionally 'soft' sciences like ecology, sociology and politics. This volume is a collection of a few cuttingedge research papers on the application of variety of computational models and tools in the analysis, interpretation and solution of vexing real-world problems and issues in economics, management, ecology and global politics by some prolific researchers in the field.
]]>
Florentin Smarandache et al.THE EFFICIENT USE OF SUPPLEMENTARY INFORMATION IN FINITE POPULATION SAMPLING
https://digitalrepository.unm.edu/math_fsp/186
https://digitalrepository.unm.edu/math_fsp/186Mon, 03 Feb 2020 08:18:21 PST
The purpose of writing this book is to suggest some improved estimators using auxiliary information in sampling schemes like simple random sampling, systematic sampling and stratified random sampling. This volume is a collection of five papers, written by nine co-authors (listed in the order of the papers): Rajesh Singh, Mukesh Kumar, Manoj Kr. Chaudhary, Cem Kadilar, Prayas Sharma, Florentin Smarandache, Anil Prajapati, Hemant Verma, and Viplav Kr. Singh. In first paper dual to ratio-cum-product estimator is suggested and its properties are studied. In second paper an exponential ratio-product type estimator in stratified random sampling is proposed and its properties are studied under second order approximation. In third paper some estimators are proposed in two-phase sampling and their properties are studied in the presence of non-response. In fourth chapter a family of median based estimator is proposed in simple random sampling. In fifth paper some difference type estimators are suggested in simple random sampling and stratified random sampling and their properties are studied in presence of measurement error. The authors hope that book will be helpful for the researchers and students who are working in the field of sampling techniques.
]]>
Florentin Smarandache et al.ON IMPROVEMENT IN ESTIMATING POPULATION PARAMETER(S) USING AUXILIARY INFORMATION
https://digitalrepository.unm.edu/math_fsp/185
https://digitalrepository.unm.edu/math_fsp/185Mon, 03 Feb 2020 08:18:17 PST
The purpose of writing this book is to suggest some improved estimators using auxiliary information in sampling schemes like simple random sampling and systematic sampling. This volume is a collection of five papers, written by eight coauthors (listed in the order of the papers): Manoj K. Chaudhary, Sachin Malik, Rajesh Singh, Florentin Smarandache, Hemant Verma, Prayas Sharma, Olufadi Yunusa, and Viplav Kumar Singh, from India, Nigeria, and USA. The following problems have been discussed in the book: In chapter one an estimator in systematic sampling using auxiliary information is studied in the presence of non-response. In second chapter some improved estimators are suggested using auxiliary information. In third chapter some improved ratio-type estimators are suggested and their properties are studied under second order of approximation. In chapter four and five some estimators are proposed for estimating unknown population parameter(s) and their properties are studied. This book will be helpful for the researchers and students who are working in the field of finite population estimation.
]]>
Florentin Smarandache et al.Neutrosophic Optimization and its Application on Structural Designs
https://digitalrepository.unm.edu/math_fsp/184
https://digitalrepository.unm.edu/math_fsp/184Mon, 03 Feb 2020 08:18:13 PST
In the real world, uncertainty or vagueness is prevalent in engineering and management computations. Commonly, such uncertainties are included in the design process by introducing simplified hypothesis and safety or design factors. In case of structural and pavement design, several design methods are available to optimize objectives. But all such methods follow numerous monographs, tables and charts to find effective thickness of pavement design or optimum weight and deflection of structure calculating certain loop of algorithm in the cited iteration process. Most of the time, designers either only take help of a software or stop the cited procedure even after two or three iterations. As for example, the finite element method and genetic algorithm type of crisp optimization method had been applied on the cited topic, where the values of the input parameters were obtained from experimental data in laboratory scale. But practically, above cited standards have already ranged the magnitude of those parameters in between maximum to the minimum values. As such, the designer becomes puzzled to select those input parameters from such ranges which actually yield imprecise parameters or goals with three key governing factors i.e. degrees of acceptance, rejection and hesitancy, requiring fuzzy, intuitionistic fuzzy, and neutrosophic optimization. Therefore, the problem of structural designs, pavement designs, welded beam designs are firstly classified into single objective and multi-objective problems of structural systems. Then, a mathematical algorithm - e.g. Neutrosophic Geometric Programming, Neutrosophic Linear Programming Problem, Single Objective Neutrosophic Optimization...
]]>
Florentin Smarandache et al.STUDY OF NATURAL CLASS OF INTERVALS USING (–∞,∞) AND (∞, –∞)
https://digitalrepository.unm.edu/math_fsp/183
https://digitalrepository.unm.edu/math_fsp/183Tue, 21 Jan 2020 10:58:43 PST
In this book the authors study the properties of natural class of intervals built using (–∞, ∞) and (∞, –∞). These natural class of intervals behave like the reals R, as far as the operations of addition, multiplication, subtraction and division are concerned. Using these natural class of intervals we build interval row matrices, interval column matrices and m × n interval matrices. Several properties about them are defined and studied. Also all arithmetic operations are performed on them in the usual way. The authors by defining so have made it easier for operations like multiplication, addition, finding determinant and inverse on matrices built using natural class of intervals. We also define polynomials with coefficients from natural class of intervals or polynomial intervals, both these concepts are one and the same, for one can be obtained from the other and vice versa. The operations of integration and differentiation are defined on these interval polynomials in a similar way as that of usual polynomials.
]]>
Florentin Smarandache et al.Multidimensional MOD Planes
https://digitalrepository.unm.edu/math_fsp/182
https://digitalrepository.unm.edu/math_fsp/182Tue, 21 Jan 2020 10:58:40 PST
In this book authors name the interval [0, m); 2 ≤ m ≤ ∞ as mod interval. We have studied several properties about them but only here on wards in this book and forthcoming books the interval [0, m) will be termed as the mod real interval, [0, m)I as mod neutrosophic interval, [0,m)g; g2 = 0 as mod dual number interval, [0, m)h; h2 = h as mod special dual like number interval and [0, m)k, k2 = (m − 1) k as mod special quasi dual number interval. However there is only one real interval (∞, ∞) but there are infinitely many mod real intervals [0, m); 2 ≤ m ≤ ∞. The mod complex modulo finite integer interval (0, m) iF; iF2= (m − 1) does not satisfy any nice properly as that interval is not closed under product . Here we define mod transformations and discuss several interesting features about them. So chapter one of this book serves the purpose of only recalling these properties.
]]>
Florentin Smarandache et al.MOD Pseudo Linear Algebras
https://digitalrepository.unm.edu/math_fsp/181
https://digitalrepository.unm.edu/math_fsp/181Tue, 21 Jan 2020 10:58:36 PST
In this book authors for the first time elaborately study the notion of MOD vector spaces and MOD pseudo linear algebras. This study is new, innovative and leaves several open conjectures. In the first place as distributive law is not true we can define only MOD pseudo linear algebras. Secondly most of the classical theorems true in case of linear algebras are not true in case of MOD pseudo linear algebras. Finding even eigen values and eigen vectors happens to be a challenging problem. Further the notion of multidimensional MOD pseudo linear algebras are defined using the notion of MOD mixed matrices. These function only under the natural product ×n as the usual product × cannot be even defined on these mixed MOD matrices.
]]>
Florentin Smarandache et al.MOD Planes: A New Dimension to Modulo Theory
https://digitalrepository.unm.edu/math_fsp/180
https://digitalrepository.unm.edu/math_fsp/180Tue, 21 Jan 2020 10:58:32 PST
In this book for the first time authors study mod planes using modulo intervals [0, m); 2 ≤ m ≤ ∞. These planes unlike the real plane have only one quadrant so the study is carried out in a compact space but infinite in dimension. We have given seven mod planes viz real mod planes (mod real plane) finite complex mod plane, neutrosophic mod plane, fuzzy mod plane, (or mod fuzzy plane), mod dual number plane, mod special dual like number plane and mod special quasi dual number plane. These mod planes unlike real plane or complex plane or neutrosophic plane or dual number plane or special dual like number plane or special quasi dual number plane are infinite in numbers. Further for the first time we give a plane structure to the fuzzy product set [0, 1) × [0, 1); where 1 is not included; this is defined as the mod fuzzy plane. Several properties are derived.
]]>
Florentin Smarandache et al.Natural Neutrosophic Numbers and MOD Neutrosophic Numbers
https://digitalrepository.unm.edu/math_fsp/179
https://digitalrepository.unm.edu/math_fsp/179Tue, 21 Jan 2020 10:58:29 PST
In this book authors answer the question proposed by Florentin Smarandache “Does there exist neutrosophic numbers which are such that they take values differently and behave differently from I; the indeterminate?”. We have constructed a class of natural neutrosophic numbers m 0I , m xI , m yI , m zI where m 0I × m 0I = m 0I , m xI × m xI = m xI and m yI × m yI = m yI and m yI × m xI = m 0I and m zI × m zI = m 0I . Here take m = 12, x = 4, y = 9 and z = 6. For more refer chapter one of this book. Thus we have defined or introduced natural neutrosophic numbers using Zm under division. Further there are more natural neutrosophic numbers in the MOD interval [0, m). This concept is thoroughly analysed in chapter two.
]]>
Florentin Smarandache et al.MOD Functions: A New Approach to Function Theory
https://digitalrepository.unm.edu/math_fsp/178
https://digitalrepository.unm.edu/math_fsp/178Tue, 21 Jan 2020 10:58:24 PST
In this book the notion of MOD functions are defined on MOD planes. This new concept of MOD functions behaves in a very different way. Even very simple functions like y = nx has several zeros in MOD planes where as they are nice single line graphs with only (0, 0) as the only zero. Further polynomials in MOD planes do not in general follows the usual or classical laws of differentiation or integration. Even finding roots of MOD polynomials happens to be very difficult as they do not follow the fundamental theorem of algebra, viz a nth degree polynomial p(x) in MOD plane or MOD intervals do not have n roots for + and × are defined on them, do not satisfy the distributive laws.
]]>
Florentin Smarandache et al.INTERVAL ALGEBRAIC BISTRUCTURES
https://digitalrepository.unm.edu/math_fsp/177
https://digitalrepository.unm.edu/math_fsp/177Tue, 21 Jan 2020 10:58:21 PST
Authors in this book construct interval bistructures using only interval groups, interval loops, interval semigroups and interval groupoids. Several results enjoyed by these interval bistructures are described. By this method, we obtain interval bistructures which are associative or non associative or quasi associative. The term quasi is used mainly in the interval bistructure B = B1 ∪ B2 (or in n-interval structure) if one of B1 (or B2) enjoys an algebraic property and the other does not enjoy that property (one section of interval structure satisfies an algebraic property and the remaining section does not satisfy that particular property). The term quasi and semi are used in a synonymous way. This book has four chapters. In the first chapter interval bistructures (biinterval structures) such as interval bisemigroup, interval bigroupoid, interval bigroup and interval biloops are introduced.
]]>
Florentin Smarandache et al.Exploring the Extension of Natural Operations on Intervals, Matrices and Complex Numbers
https://digitalrepository.unm.edu/math_fsp/176
https://digitalrepository.unm.edu/math_fsp/176Tue, 21 Jan 2020 10:58:16 PST
This book extends the natural operations defined on intervals, finite complex numbers and matrices. The intervals [a, b] are such that a ≤ b. But the natural class of intervals [a, b] introduced by the authors are such that a ≥ b or a need not be comparable with b. This way of defining natural class of intervals enables the authors to extend all the natural operations defined on reals to these natural class of intervals without any difficulty. Thus with these natural class of intervals working with interval matrices like stiffness matrices finding eigenvalues takes the same time as that usual matrices. Secondly the authors introduce the new notion of finite complex modulo numbers just defined as for usual reals
]]>
Florentin Smarandache et al.Algebraic Structures on MOD Planes
https://digitalrepository.unm.edu/math_fsp/175
https://digitalrepository.unm.edu/math_fsp/175Tue, 21 Jan 2020 10:58:12 PST
Study of MOD planes happens to a very recent one. Authors have studied several properties of MOD real planes Rn(m); 2 ≤ m ≤ ∞. In fact unlike the real plane R × R which is unique MOD real planes are infinite in number. Likewise MOD complex planes Cn(m); 2 ≤ m ≤ ∞, are infinitely many. The MOD neutrosophic planes RnI(m); 2 ≤ m ≤ ∞ are infinite in number where as we have only one neutrosophic plane R(I) = 〈R ∪ I〉 = {a + bI | I2 = I; a, b ∈ R}. Further three other new types of MOD planes constructed using dual numbers, special dual number like numbers and special quasi dual numbers are introduced. Rng(m) ={a + bg | g2 = 0, a, b ∈ [0, m)} is the MOD dual number plane.
]]>
Florentin Smarandache et al.