Infinite Population Research Articles

Meridian convergence: An alternate methodology

Abstract This study investigates the development and testing of an approximation method for the Mine Surveyor to calculate meridian convergence. This study, a detailed review of experimental techniques, follows a statistical experimental approach to establish how accurate an alternative method performs against traditional methods of meridian convergence calculation used by the Mine Surveyor. The spatial study is defined by the geographical range of the existing Schreiber Geodetic Tables, ranging from 70 km south of Ndola (Zambia) to 10 km north of De Aar (South Africa). The sample size is established under the constraint of an infinite population. Linear regression in collaboration with the hold-out validation technique is adopted to statistically refine the alternative method of calculation. The computational outcomes of the refined alternative method in comparison to the unrefined method are predominantly closer to the traditional outcomes. Computational outcomes specific to the hold-out validation set demonstrate a maximum sub- 1 ″ {1^{\prime\prime }} variance of 0.650 ″ {0.650^{\prime\prime }} . A sub-variance of 0.650 ″ {0.650^{\prime\prime }} satisfies the South African Mine Survey limits of error. The subsequent clustering of variances at specific variance intervals are similar to comparative studies conducted by T. Soler and R.J. Fury with respect to meridian convergence.

Technology choice in an evolutionary oligopoly game

In this paper, we propose and analyze a two-stage oligopoly game in which firms first simultaneously choose production technologies and in the second stage simultaneously choose production quantities. After characterizing the Nash equilibrium of the game, we cast our static model in a dynamic setting exploring the stability properties of the market equilibrium in two different cases: (i) exogenously distributed technologies and Cournot adjustments and (ii) endogenously distributed technologies in an infinite population game with Cournot–Nash equilibrium outputs. The main aim of the paper is that of extending the results about Cournot oligopoly stability in an evolutionary setting of heterogeneous decreasing returns-to-scale technologies. We show how the interplay between production decisions and R&D decisions can generate endogenous market fluctuations leading to complex dynamic phenomena.

The exact solution of the mutator model with directed mutations, linear fitness function, and finite genome length

In this study, we considered the model by Beckman and Loeb [Proc. Natl. Acad. Sci. U.S.A. 103 (2006) 14140] for the mutator phenomena. We construct an infinite population Crow-Kimura model with a mutator gene, directed mutations, a linear fitness function, and a finite genome length. We solved analytically the dynamics of the model using the generating function method. Such models provide realistic predictions for finite population sizes and have been widely discussed recently. The analytical formulas provided can be used to calculate the advantage of the mutator mechanism for the accumulation of mutations in cancer biology.

Factors Influencing the Choice of Mobile Network Operator Among University Students

Background: Despite recent liberalization of the Ugandan telecommunications sector, accompanied by price reductions, improve service provision, and ease of access to Mobile phones, there still exists wide gap in market share amongst the telecom operators in Uganda. The telecom operators include MTN, Airtel, Africell and others. The youth in Uganda, specifically the university students, have been discovered to be the largest adopters to internet service innovations a technology making; thus contributing an enormous percentage to the Ugandan mobile telephony market. Data source: Data was collected from the respondents using a carefully designed structured questionnaire with open and closed ended questions. The study used both qualitative and quantitative data analysis techniques. Methods: Cochran’s formula for infinite populations was used to come up with a sample size, and stratified simple random sampling was applied to select respondents from the target population. Three independent logistic regressions were fit to each of the choice of the network operators, with choice under analysis taking the value of 1 and others assuming 0. Results: Price, service quality, promotional activities, and peer influence were the factors that influenced students’ choice of mobile network operator. Price came out as the most important factor, followed by service quality, service availability, peer influence and finally promotional activities. Airtel had the largest number of subscriptions among the university students, followed by MTN, then finally Africell. Conclusions: Network operators should focus on establishing sound pricing strategies, and developing products that are well profiled according to student characteristics such as age and duration of use, to better understand student market segments in order to increase patronage, and capture more new student customers. Government agencies should also set basic minimum network standards such as service quality. This kind of study and other questions can be extended at regional level to provide further impetus for developing of policies to improve revenues from the Ugandan Telecommunications Industry.

Self-regulation in infinite populations with fission-death dynamics

The evolution of an infinite population of interacting point entities placed in Rd is studied. The elementary evolutionary acts are death of an entity with rate that includes a competition term and independent fission into two entities. The population states are probability measures on the corresponding configuration space and the result is the construction of the evolution of states in the class of sub-Poissonian measures, that corresponds to the lack of clusters in such states. This is considered as a self-regulation in the population due to competition.

DESIGNED EXPERIMENTS: DO YOU KNOW WHAT POPULATION YOU ARE SAMPLING FROM?

SUMMARYConsider a field experiment laid out in a randomized complete block design in which you study three types of fertilizers for two winter wheat cultivars. One year, one location – the experiment is not repeated. You design it and then spend a lot of time and money to conduct it. You cultivate the soil and take care of the plants; you worry about them; you never know what can happen, so you cannot wait for the crop to be harvested. And that day finally comes. The crop is harvested, and everything is fine. And here you are, all went great, you have the data in hands, and now a simple thing to do – analyse them. Well, yes, the experiment was conducted in one year, and you are aware you cannot be sure the outcome would be the same next year or elsewhere, but whatever – suffice it to consider the conclusions as preliminary and get on with the interpretation. Why should you not? It was a properly designed experiment that took samples from the underlying infinite populations of the two winter wheat cultivars in the three water regimes studied. Statistics is here to help you out, is not it? Well, it is not. Statistics will not help you out whether the experiment was poorly designed. Agricultural science literature seldom explains what populations are studied and what types of samples are taken in designed experiments. To fill this gap, we discuss various aspects of the sampling process in designed experiments. In doing so, we look at the survey sampling methodology, a statistical framework for studying finite populations – we do this because survey sampling has developed into the advanced theory of sampling processes, and this background can help us understand the intrinsic aspects of sampling in designed experiments.

Health Practices and Longevity: A Study of the Elderly in Akwa Ibom State, Nigeria

Health practices are patterns of behavioural choices made by an individual from the alternatives that are available according to their socio-economic status. The UNDESA report gives the life expectancy for Nigerians to be below 54 years. We re-examine the 2015 UNDESA report vis-a-vis the health practices of the Elderly in Nigeria using Akwa Ibom State as reference. The study adopted descriptive survey design and using the multistage sampling technique purposively identify and included men and women aged 65 and above. A total of 24 local government areas were covered in this study and a sample size of 384 respondents were selected using the Bill Godden formula for infinite population. Data collected were analysed using the descriptive statistics The findings showed that 39 percent of the respondents were between 70-74 years. From the correlation matrix, there was a significant relationship between Nutrition and food intake and longevity. Improvement in the socio–economic status of the elderly by regular payment of their pension; as well as increased attention to their health by relevant individuals and groups among other measures that will further promote their longevity are strongly recommended.

THE EFFECT OF BRAND IMAGE AND FOOD SAFETY ON THE PURCHASE DECISION OF SAMYANG NOODLES PRODUCT TO THE STUDENTS OF FACULTY OF ECONOMICS AND BUSINESS OF UNIVERSITY OF NORTH SUMATRA MEDAN

This research aims to attract and maintain consumer loyalty in purchasing products. This type of research is quantitative research. The p rab urpose of this research is to know and to analyze the influence of brand image to the purchase decision of Samyang noodle product, the influence of food safety to the purchase decision of Samyang noodle product, the influence of brand image and food safety toward the decision of Samyang noodles product to the students of Faculty of Economics and Business University of North Sumatera Medan. This research uses explanative method. Esplanative research aims to understand why a variable can lead to the emergence of a certain effect or effect. Explanative research also aims to explain the picture of a condition, the characteristics of a phenomenon or object that explains the relationship between variables. The population of this study is all students of Strata-1 Faculty of Economics and Business University of North Sumatra who had bought the product of Samyang noodles. This population is an infinite population (indefinite) because the number of buyers of different products Samyang every day. The sample in this research is 97 students of Faculty of Economics and Business University of North Sumatera Medan by using Lemeshow formula. Sampling technique in this research is non-probability sampling by using incidental sampling. The data collection techniques used in this study are questionnaires and documentation. The results showed partial results, brand image significantly influence purchasing decisions, and food safety have an effect but not significant to purchasing decision. Simultaneously, the result of the research shows that brand image and food safety have significant effect on purchasing decision. Keywords: Brand Image, Food Safety and Purchasing Decisions

Bootstrap Variance Estimation for Semiparametric Finite Population Distribution Function Estimator

Estimating finite population distribution function (FPDF) emerges as an important problem to the survey statisticians since the pioneering work of Chambers and Dunstan [1] . It unifies estimation of standard finite population parameters, namely, mean and quantiles. Regarding this, estimating variance of FPDF estimator is an important task for accessing the quality of the estimtor and drawing inferences (e.g., confidence interval estimation) on finite population parameters. Due to non-linearity of FPDF estimator, resampling-based methods are developed earlier for parametric or non-parametric Chambers–Dunstan estimator. Here, we attempt the problem of estimating variance of P-splines-based semiparametric model-based Chambers–Dunstan type estimator of the FPDF. The proposed variance estimator involes bootstrapping. Here, the bootstrap procedure is non-trivial since it does not imitate the full mechanism of two-stage sample generating procedure from an infinite hypothetical population (superpopulation). We have established the weak consistency of the proposed resampling-based variance estimator for specific sampling designs, e.g., simple random sampling. Also, the satisfactory empirical performance of the poposed estimator has been shown through simulation studies and a real life example.

On optimal policy in the group testing with incomplete identification

Consider a very large (infinite) population of items, where each item independent from the others is defective with probability p, or good with probability q=1−p. The goal is to identify N good items as quickly as possible. The following group testing policy (policy A) is considered: test items together in the groups, if the test outcome of group i of size ni is negative, then accept all items in this group as good, otherwise discard the group. Then, move to the next group and continue until exact N good items are found. The goal is to find an optimal testing configuration, i.e., group sizes, under policy A, such that the expected waiting time to obtain N good items is minimal. Recently, Gusev (2012) found an optimal group testing configuration under the assumptions of constant group size and N=∞. In this note, an optimal solution under policy A for finite N is provided.

Analysis of multi server Markovian queue with functioning vacation and intolerance of customer

In this article, we analyze the operating behavior of two server Markovian queueing model with functioning vacation and infinite population. If the server is halt his service suddenly in a normal busy period and repair work is done immediately and service starts. The server failure and repair rates are follow exponential distribution, when the system become vacation the server takes functioning during this period the customer wait in the queue and server serves the customer with the lower service rate. The steady state behavior is also obtained, the various performance measures are also determined. The numerical example is given to test the feasibility of the model.

Front propagation and clustering in the stochastic nonlocal Fisher equation.

In this work, we study the problem of front propagation and pattern formation in the stochastic nonlocal Fisher equation. We find a crossover between two regimes: a steadily propagating regime for not too large interaction range and a stochastic punctuated spreading regime for larger ranges. We show that the former regime is well described by the heuristic approximation of the system by a deterministic system where the linear growth term is cut off below some critical density. This deterministic system is seen not only to give the right front velocity, but also predicts the onset of clustering for interaction kernels which give rise to stable uniform states, such as the Gaussian kernel, for sufficiently large cutoff. Above the critical cutoff, distinct clusters emerge behind the front. These same features are present in the stochastic model for sufficiently small carrying capacity. In the latter, punctuated spreading, regime, the population is concentrated on clusters, as in the infinite range case, which divide and separate as a result of the stochastic noise. Due to the finite interaction range, if a fragment at the edge of the population separates sufficiently far, it stabilizes as a new cluster, and the processes begins anew. The deterministic cutoff model does not have this spreading for large interaction ranges, attesting to its purely stochastic origins. We show that this mode of spreading has an exponentially small mean spreading velocity, decaying with the range of the interaction kernel.

English

The study focuses on the psychological theory of colour in graphic design on the advertisement of consumer goods. The specific objectives identify the impact of colour perception and emotion as it psychologically affects and influences the behaviour of consumers in purchasing the products advertised. Descriptive research study, that is, employing qualitative methodology was used to address the study and it adopted survey design method to investigate the activities of the respondents (the consumers) that emotion and colour have impacts on their purchasing behaviour. The population for consumers is infinite and outside the limit of manageable size. Yamane‟s formula which stated that a finite population consists of a fixed number of elements that can be easily counted, while an infinite population on the other hand is where a complete count of all element or subject that makes up the population cannot possibly be counted was therefore adopted to determine the sample size of three hundred and eighty-five (385). Random sampling method was used in administration of the questionnaire and structured questionnaire was used to collect demographic information about the respondents and elicited responses from the respondents on issues raised in research questions and the objectives of the research. Frequency and percentage distribution were used to analyse the background information of the respondents and some of the issues addressed in the questionnaire. The result of the analysis established that colour value and emotional theory stimulate and energize consumers, and that it creates acceptance, admiration, affection and psychologically served as powerful market tools. A consumer Colour Perception Purchasing Behaviour Model was proposed based on the result. Key words: Psychoanalytical, emotion, colour value, consumer, theory, graphics. &nbsp

PRICE PERCEPTION: EFFECT OF COUPON PRONENESS AND SALE PRONENESS ON CONSUMER IMPULSE BUYING

The purpose of this research is to find out the consumer’s price perception by considering two factors, namely coupon proneness and sale proneness in order to know its influences on impulse buying of the consumer from one of the biggest department store retail company in Surabaya. Then, the researcher needs to take 385 respondents, which are taken from the infinite population of the department store’s consumer by utilizing questionnaire as a research instrument.The research is quantitative with the data analysis applies multiple regressions by using SPSS program. By the research, the researcher applies independent and dependent variables. The independent variable consists of coupon proneness and sale proneness. The dependent variable consists of impulse buying. The result of the research shows that there is a simultaneous effect of coupon proneness and sale pronenesstowardimpulse buying, however, there is no significant partially effect of sale proneness towards impulse buying. There are also many factors besides coupon proneness and sale proneness which also influence consumer impulse buying.

Replicator dynamics for public goods game with resource allocation in large populations

Costly punishment can promote human cooperation, but the effectiveness of punishment is reduced because of the existence of second-order free-rider problem. How to solve the problem remains a challenge for the emergence of costly punishment. Motivated by the regimes of resource allocation in human society, in this work we consider the resource allocation with threshold for the common pool in the public goods game with an additional strategy of peer punishment, and aim to explore whether such proposed resource allocation can solve the problem of second-order free-riders by using replicator equations in infinite well-mixed populations. We assume that if contributing resources in the common pool exceed the threshold, the contributing resources will be divided into two parts: the first part will be equally allocated by all the players, and the second part will be allocated by all the players based on their strategy choices. Otherwise all the contributing resources are equally allocated by all the players. We find that the second-order free-rider problem can be effectively solved by this regime of resource allocation even when most of contributing resources are equally allocated among individuals. In addition, we find that punishment is the dominant strategy in a broad region of allocation parameters. Our work may thus suggest an effective approach about resource allocation for resisting second-order free-riders in the public goods dilemma.

Which is more effective for suppressing an infectious disease: imperfect vaccination or defense against contagion?

We consider two imperfect ways to protect against an infectious disease such as influenza, namely vaccination giving only partial immunity and a defense against contagion such as wearing a mask. We build up a new analytic framework considering those two cases instead of perfect vaccination, conventionally assumed as a premise, with the assumption of an infinite and well-mixed population. Our framework also considers three different strategy-updating rules based on evolutionary game theory: conventional pairwise comparison with one randomly selected agent, another concept of pairwise comparison referring to a social average, and direct alternative selection not depending on the usual copying concept. We successfully obtain a phase diagram in which vaccination coverage at equilibrium can be compared when assuming the model of either imperfect vaccination or a defense against contagion. The obtained phase diagram reveals that a defense against contagion is marginally inferior to an imperfect vaccination as long as the same coefficient value is used.Highlights– We build a new analytical framework for a vaccination game combined with the susceptible-infected-recovered (SIR) model.– Our model can evaluate imperfect provisions such as vaccination giving only partial immunity and a defense against contagion.– We obtain a phase diagram with which to compare the quantitative effects of partial vaccination and a defense against contagion.

English

The essence of most investments is quality return. Continuous quality returns are guaranteed by patronages enjoyed by the investment, this therefore sustains the business. Hardly has this been achieved by most patrol stations that litter the roads of Anambra state of Nigeria due to the location of such businesses. Pursuant to the aforementioned problem, the study seeks to ascertain the extent to which business development relates to sustainability of petrol stations in Anambra state of Nigeria. The paper is anchored on the ‘Central Place Theory’. The population of this study consists of the customers who patronize these petrol stations in Anambra state. The study specifically identified the extent of relationship that exists between location and service sustainability of selected petrol stations. The research question and hypothesis were formulated in line with the specific objective. Infinite population was used because customers that visit the petrol stations cannot be determined, and sample size was determined using Z score for infinite population. Pearson Product Moment Correlation was used to test the hypothesis. The study revealed that there is a significant positive relationship between location and service sustainability of these petrol stations. Based on the finding, the study recommended that relevant regulatory bodies should enforce the compliance of the rules and regulations of Department of Petroleum Resources on location of petrol stations in the state to ensure improvement in the sustainability of these petrol stations. Key words: Business development, sustainability, central placed theory, Nigeria.

Modelo de Regresión Logística Multinomial para medir las preferencias que tienen los clientes en el sector farmacéutico: caso Ambato, Ecuador

Context: The investigation includes the Ecuadorian pharmaceutical market from the business competitive point of view, focusing on the service offered by the Farmacias Cruz Azul and Farmacias Económicas franchises. Aims: To determine the main variables that influence the consumer's choice, in the pharmaceutical sector, and generate a predictive model of competitive analysis. Methods: Through the Multinomial Logistic Regression Model was obtained the significant variables that helped to predict the customer’s pharmacy choice. The study was conducted in the zone number 3, center of the country, whose sample was calculated based on the infinite population formula. A total of 393 clients were surveyed in the main public and private health centers. Results: After establishing the dependent variable "Choice of Pharmacy"; Of the eight variables under study, the relevant independent variables were: Reason for choice, Fidelity and Low prices with a level of significance of 0.003, 0.001 and 0.000, respectively. Final variables and introduced to the regression model; which resulted, a probability of 16.82% that customers go to Farmacias Cruz Azul, 77.12% to choose Farmacias Económicas, and only 0.63% to go to another pharmacy, including independent. Conclusions: The Multinomial Logistic Regression Model was useful to predict the probability of choice of pharmacy, which a client has according to variables that represent service; allowing also to perform key simulations for the continuous improvement of the sector, planning and competitive analysis.

Analyzing imperfective games

Deo 2015 is the first study applying mathematically explicit evolutionary analysis to a specific semantic-change phenomenon, namely the progressive-imperfective diachronic cycle. However, Deo’s actual results do not match completely the empirical observations about that cycle. Linguistic communities passing through the cycle often employ, in the synchrony, a single common type of progressive-imperfective grammar. In Deo’s modeling results, however, two of the grammars never get shared by nearly all the population, including the grammar with the obligatory use of progressive marking in semantically progressive contexts, as in Present-Day English. This paper improves on that wrong prediction. The crucial modeling decision enabling the improvement is switching from the assumption of infinite speaker population to the more realistic, but harder to analyze finite population setting. The finite-population version of Deo’s model derives stages where at many time points, all or almost all speakers share the same grammar. Interestingly, two different a priori reasonable types of trajectories with that feature emerge, depending on the parameter settings. These two trajectory types constitute novel empirical predictions regarding the shape of the cycle generated by (the proposed extension of) Deo’s model. Supplementary materials (SM 1 and SM 2) BibTeX info

Frequency-dependent growth in class-structured populations: continuous dynamics in the limit of weak selection.

In this paper we consider class-structured populations in discrete time in the limit of weak selection and with the inverse of the intensity of selection as unit of time. The aim is to establish a continuous model that approximates the discrete model. More precisely, we study frequency-dependent growth in an infinite haploid population structured into a finite number of classes such that individuals in each class contribute to a given subset of classes from one time step to the next. These contributions take the form of generalized fecundity parameters with perturbations of order 1/N that depends on the class frequencies of each type and the type frequencies. Moreover, they satisfy some mild conditions that ensure mixing in the long run. The dynamics in the limit as [Formula: see text] with N time steps as unit of time is considered first in the case of a single type, and second in the case of multiple types. The main result is that the type frequencies as [Formula: see text] obey the replicator equation with instantaneous growth rates for the different types that depend only on instantaneous equilibrium class frequencies and reproductive values. An application to evolutionary game theory complemented by simulation results is presented.