Naushad Ali Mamode Khan

University of Mauritius | UoM · Department of Economics and Statistics

This article introduces and investigates the Marshall-Olkin Topp-Leone log-normal (MOTLLN) distribution, a novel extension of the log-normal distribution. It can be presented as a new four-parameter continuous distribution designed to analyze a wide range of versatile positive-valued data. In a brief first part, we explore its main aspects, includi...

The literature on discrete valued time series is expanding very fast. Very often we see new models with very similar properties to the existing ones. A natural question that arises is whether the multitude of models with very similar properties can really have a practical purpose or if they mostly present theoretical interest. In the present paper,...

This paper introduces a non-stationary bivariate integer-valued auto-regressive process of order p (BINAR(p) with non-stationary moments. The BINAR(p) uses the conventional binomial thinning procedure and the cross correlation between the two related series is induced from the paired innovation terms. The conditional maximum likelihood (CML) approa...

In spatial count data analysis, modeling with a multilateral lattice structure presents some important challenges. They include both the model construction and the estimation of the model parameters, since the structure accommodates the left, right, top, bottom, and diagonal site effects. Thus, the multilateral spatial process unifies all the popul...

This paper proposes a novel Bivariate integer-valued auto-regressive model of order 1 with paired Poisson Weighted Exponential (PWE) distributed innovations which is denoted by INAR(1)-PWE with two Sarmanov and classical versions. The CML and CLS estimators of the parameters are obtained and the performance of the proposed models are assessed throu...

The modified (or second version) gamma kernel of Chen [Probability density func- tion estimation using gamma kernels, Annals of the Institute of Statistical Math- ematics 52 (2000), pp. 471–480] should not be automatically preferred to the stand- ard (or first version) gamma kernel, especially for univariate convex densities with a pole at the orig...

The modified (or second version) gamma kernel of Chen [Probability density function estimation using gamma kernels, Annals of the Institute of Statistical Mathematics 52 (2000), pp. 471–480] should not be automatically preferred to the standard (or first version) gamma kernel, especially for univariate convex densities with a pole at the origin. In...

Based on the well-known Poisson (P) distribution and the new generalized Lindley distribution (NGLD) developed by using gamma (α,θ) and gamma (α-1,θ) distributions, a new compound two-parameter Poisson generalized Lindley (TPPGL) distribution is proposed in this paper and thereon systematically explores the mathematical properties. Closed form expr...

This paper introduces a flexible discrete transmuted record type discrete Burr–Hatke (TRT-DBH) model that seems suitable for handling over-dispersion and equi-dispersion in count data analysis. Further to the elegant properties of the TRT-DBH, we propose, in the time series context, a first-order integer-valued autoregressive process with TRT-DBH d...

This paper proposes a new flexible discrete triplet Lindley model that is constructed from the balanced discretization principle of the extended Lindley distribution. This model has several appealing statistical properties in terms of providing exact and closed form moment expressions and handling all forms of dispersion. Due to these, this paper e...

Over the past few years, interest has increased in models defined on positive and negative integers. Several application areas lead to data that are differences between positive integers. Some important examples are price changes measured discretely in financial applications, pre- and posttreatment measurements of discrete outcomes in clinical tria...

Discrete-valued time series modeling has witnessed numerous bivariate first-order integer-valued autoregressive process or BINAR(1) processes based on binomial thinning and different innovation distributions. These BINAR(1) processes are mainly focused on over-dispersion. This paper aims to propose new bivariate distributions and processes based on...

In this paper, the first-order non-negative integer-valued autoregressive process with Poisson-transmuted exponential innovations is introduced. Three estimation methods, namely, the conditional maximum likelihood, conditional least squares and Yule-Walker estimation methods are discussed to estimate the unknown parameters of the proposed process....

This paper deals with the study of some probabilistic and statistical properties of a Periodic Integer-Valued Moving Average Model (PINMAS(q)) with Generalized Poisson and Negative Binomial innovation process, for modelling di¤erent types of dispersion in count time series. Some probabilistic properties of the process are obtained. Furthermore, the...

For this 3rd LmB conference at Besançon from 06 to 08 July 2022, there are twenty two Titles and Abstracts provided by their authors that we sincerely thank.

The COVID-19 series is obviously one of the most volatile time series with lots of spikes and oscillations. The conventional integer-valued auto-regressive time series models (INAR) may be limited to account for such features in COVID-19 series such as severe over-dispersion, excess of zeros, periodicity, harmonic shapes and oscillations. This pape...

In this paper, we introduce a new stationary first-order integer-valued autoregressive process (INAR) with zero-and-one-inflated geometric innovations that is useful for modeling medical practical data. Basic probabilistic and statistical properties of the model are discussed. Conditional least squares and maximum likelihood estimators are proposed...

Purpose The purpose of this study is to investigate whether the corporate environmental, social and governance (ESG) performance of companies is influenced by the barriers and opportunities created by three factors characterising a country’s governance landscape: democracy, political stability and regulatory quality. Additionally, this study separa...

A modified gamma kernel should not be automatically preferred to the standard gamma kernel, especially for univariate convex densities with a pole at the origin. In the multivariate case, multiple combined gamma kernels, defined as a product of univariate standard and modified ones, are here introduced for nonparametric and semiparametric smoothing...

This paper proposes some high-ordered integer-valued auto-regressive time series process of order p (INAR(p)) with Zero-Inflated and Poisson-mixtures innovation distributions, wherein the predictor functions in these mentioned distributions allow for covariate specification, in particular, time-dependent covariates. The proposed time series structu...

Background: Female breast cancer (FBC) is a public health issue which represents the third leading cause of deaths in Mauritius (accounting for 13.5% of all the deaths in 2017), after diabetes and cardiovascular diseases. The present research aimed to identify the potential causative factors associated with FBC in Mauritius, given the genetic polym...

In this paper, two-parameter Poisson binomial-exponential 2 (PBE2) distribution is firstly reviewed, then a new integer-valued autoregressive (INAR) model with PBE2 innovations is proposed. The definition and statistical properties of the proposed model are given, including the mean, variance, covariance, strict stationarity and ergodicity. Two-ste...

The ridge regression estimator is a commonly used procedure to deal with multicollinear data. This paper proposes an estimation procedure for high-dimensional multicollinear data that can be alternatively used. This usage gives a continuous estimate, including the ridge estimator as a particular case. We study its asymptotic performance for the gro...

The ridge regression estimator is a commonly used procedure to deal with multicollinear data. This paper proposes an estimation procedure for high-dimensional multicollinear data that can be alternatively used. This usage gives a continuous estimate, including the ridge estimator as a particular case. We study its asymptotic performance for the gro...

Undeniably, the Novel Coronavirus 2019, (COVID-19), has disrupted the routine functioning of the global economic and social activities. In particular, vulnerable economies such as the Small Island Developing states (SIDs) are facing unprecedented health and financial crisis. In such critical situation, some in-depth statistical models can be helpfu...

A correction to this paper has been published: https://doi.org/10.1007/s42452-021-04401-1

In this paper, we introduce a new general family of skewed distributions obtained through the use of a weighted skewed technique. This technique has the feature to unify two classical skewness techniques. Also, it is based on a clear stochastic representation involving a tuning weight function. General moments results are given. Subsequently, we fo...

This paper introduces a first-order integer-valued autoregressive process with a new innovation distribution, shortly INARPQX(1) process. A new innovation distribution is obtained by mixing Poisson distribution with quasi-xgamma distribution. The statistical properties and estimation procedure of a new distribution are studied in detail. The parame...

We consider models for count variables with a GARCH-type structure. Such a process consists of an integer-valued component and a volatility process. Us- ing arguments for contractive Markov chains we prove that this bivariate process has a unique stationary regime. Furthermore, we show absolute regularity (β-mixing) with geometrically decaying coef...

This article proposes a nonstationary clustered longitudinal model to analyze road traffic accident time series data from 2016 to 2017 in Mauritius. The Conway–Maxwell–Poisson model (COM-Poisson) is used as the baseline model with gamma-distributed random effects (CMP-G). Several time-variant explanatory variables are incorporated into the model sp...

In classical linear regression analysis problems, the ordinary least-squares (OLS) estimation is the popular method to obtain the regression weights, given the essential assumptions are satisfied. However, often, in real-life studies, the response data and its associated explanatory variables do not meet the required conditions, in particular under...

Mauritius stands as one of the few countries in the world to have controlled the current pandemic, the novel coronavirus 2019 (COVID-19) to a significant extent in a relatively short lapse of time. Owing to uncertainties and crisis amid the pandemic, as an emergency announcement, the World Health Organization (WHO) solicits the help of health autho...

We consider integer-valued GARCH processes, where the count variable conditioned on past values of the count and state variables follows a so-called Skellam distribution. Using arguments for contractive Markov chains we prove that the process has a unique stationary regime. Furthermore, we show asymptotic regularity ($\beta$-mixing) with geometrica...

This paper considers modelling of a non‐stationary bivariate integer‐valued autoregressive process of order 1 (BINAR(1)) where the cross‐dependence between the counting series is formed through the relationship of the current series with the previous‐lagged count series observations while the pair of innovations is independent and marginally Poisso...

In this paper, we review INMA time series of integer-valued model class, and discuss its further development. These models have been developed for analyzing high frequency financial count data. A vivid description of high frequency data in the context of market micro structure is given. The most distinguishing feature that makes the INMA model clas...

In the literature of discrete-valued time series modelling, various bivariate integer-valued autoregressive time series models of order 1 (BINAR(1)) have been proposed particularly based on the binomial thinning mechanism and with different innovation distributions. These BINAR(1)s are mostly suitable for modelling bivariate counting series of vari...

In particular, this paper addresses solutions to the computational challenges encountered in estimating parameters in non-stationary over-dispersed bivariate integer-valued autoregressive of order 1 (BINAR(1)) model with Negative Binomial (NB) innovations. In this BINAR(1) model, the cross-correlation is induced through the paired NB innovations wh...

The ranking of some English Premier League (EPL) clubs during football season is of keen interest to many stakeholders with special attention to the London rivals: Arsenal, Chelsea and Tottenham. In particular, the first (GF) and second half (GS) scores, besides being inter-related, is perceived as a convenient measure of the clubs potential. This...

While most of the literature about INARMA models (integer-valued autoregressive moving-average) concentrates on the purely autoregressive INAR models, we consider INARMA models that also include a moving-average part. We study moment properties and show how to efficiently implement maximum likelihood estimation. We analyze the estimation performanc...

This paper proposes a new generator function based on the inverted Kumaraswamy distribution and introduces ‘generalized inverted Kumaraswamy-G’ family of distributions. We provide a comprehensive account of some of its mathematical properties that include the ordinary and incomplete moments, quantile and generating functions and order statistics. T...

Background The prevalence of type 2 diabetes mellitus (T2DM) is increasing at an alarming rate in developing countries. The accompanying complications of T2DM can be reduced by maintaining a good adherence to medication and self-care activities. Objectives To evaluate medication adherence and self-care behaviors among patients with T2DM. Methods...

Objectives: To validate, from a psychometric perspective, the Problem Areas in Diabetes (PAID)questionnaire in patients with type 2 diabetes mellitus from Malaysia. Methods: A total of 497 patients with type 2 diabetes mellitus were recruited from public hospitals in the state of Selangor through convenience sampling. Construct validity was evaluat...

This paper introduces Quasi-Maximum Likelihood Estimation for Long Memory Stock Transaction Data of unknown underlying distribution. The moments with conditional heteroscedasticity have been discussed. In a Monte Carlo experiment, it was found that the QML estimator performs as well as CLS and FGLS in terms of eliminating serial correlations, but t...

The existing stationary bivariate integer-valued autoregressive model of order 1 (BINAR(1)) with correlated Negative Binomial (NB) innovations is capable of modelling stationary count series where the innovation terms of both series have same over-dispersion index. Such BINAR(1) may not be useful to model real-life series that are affected by commo...

This article addresses the modelling of day and night larceny incidents in two regions of Mauritius through a bivariate integer-valued autoregressive of order 1 (BINAR(1)) model with a flexible Conway–Maxwell Poisson (CMP) innovations under time-varying moments. The outcome of the study demonstrates scientifically the contributory effects and helps...

This paper proposes a non-stationary bivariate integer-valued moving average of order 1 (BINMA(1)) model where the respective innovations are marginal COM-Poisson and unrelated. As opposed to other such bivariate time series model, the dependence between the series in the above is constructed via the relation between the current series with survivo...

This paper investigates on the sun’s activity based on sunspot images using time series of sunspot numbers and absolute 10.7 cm flux that would also enable to establish relationship between these indices and provide possible forecasts. Moreover, these indices are also compared with the monthly number of solar bursts detected by the Mauritian Radio...

The problem of multicollinearity among predictor variables is a frequent issue in longitudinal data analysis. In this context, this paper proposes a mixed ridge regression model via shrinkage methods to analyze such data. Furthermore, in view of obtaining more efficient estimators, we propose preliminary and Stein-type estimators using prior inform...

The article introduces a first-order bivariate integer-valued moving average process (BINMA(1)) where the respective innovation series are marginally COM-Poisson distributed under nonstationary moments. The purpose of this process is to model inter-related INMA(1) time series that are known to exhibit different levels and types of dispersion. The u...

This article proposes a first order integer-valued moving average (INMA(1)) process where the innovations are COM-Poisson under non-stationary moments. In this set-up, the non-stationary is induced through time-dependent covariates. However, the corresponding marginal distribution of the counting series is rather difficult to specify and, hence, th...

This paper introduces a non-stationary bivariate integer-valued moving average of first-order (BINMA(1)) model with corresponding negative binomial innovations under different levels of over-dispersion that are pairwise unrelated. In the proposed BINMA(1), the interrelation between the series is induced by the relation of the current observation wi...

It is commonly observed in medical and financial studies that large volume of time series of count data are collected for several variates. The modelling of such time series and the estimation of parameters under such processes are rather challenging since these high dimensional time series are influenced by time-varying covariates that eventually...

This paper focuses on the factors that influence the Mauritian automobile insurance claims; a process known as automobile ratemaking. The response variables are the average claim frequency counts and the claim severity. These two components are then combined to provide the pure premium. Generalized Linear Models are used to measure the influence of...

In this paper a technique is developed to improve performance of multi-layer neural networks in their learning process. Learning rate is one of the important parameters in learning process of neural networks. Inappropriate learning rate reduces the convergence rate. We have developed a technique to adaptively set the learning rate during the learni...

Purpose Undeniably, the growing influence of technology has had a significant impact on the reading process of undergraduate students and it is thus of priority interest now to understand the factors influencing independent and digital reading. The paper aims to discuss these issues. Design/methodology/approach In total, 231 questionnaires were...

This paper focuses on the modeling of the intra-day transactions at the Stock Exchange Mauritius (SEM) of the two major banking companies: Mauritius Commercial Bank Group Limited (MCB) and State Bank of Mauritius Holdings Ltd (SBMH) in Mauritius using a flexible non-stationary bivariate integer-valued moving average of order 1 (BINMA(1)) process wi...

Diabetes self-care activities is an important aspect for Type 2 Diabetes Mellitus (T2DM) patients. The aim of this study was to examine the construct validity of the Summary of Diabetes Self-Care Activities (SDSCA) measure. This was a cross-sectional study whereby T2DM patients were recruited from endocrine clinics in hospitals. The patients gave t...

Time series of counts occur in many real-life situations where they exhibit various forms of dispersion. To facilitate the modeling of such time series, this paper introduces a flexible first-order integer-valued non-stationary autoregressive (INAR(1)) process where the innovation terms follow a Conway-Maxwell Poisson distribution (COM-Poisson). To...

This paper introduces an observation-driven (OD) longitudinal integer-valued moving average model of order 1 (INMA(1)) with COM–Poisson innovations under non-stationary moment conditions. This new longitudinal model provides lot of practical flexibility in terms of modeling a wide range of over-, under-dispersion and any mixed level of dispersion....

In a recent research, the quasi-likelihood estimation methodology was developed to estimate the regression effects in the Generalized BINMA(1) (GBINMA(1)) process. The method provides consistent parameter estimates but, in the intermediate computations, moment estimating equations were used to estimate the serial- and cross-correlation parameters....

Real count data time series often show the phenomenon of the overdispersion. In this paper, we introduce a first order non-negative integer valued autoregressive process with Poisson-Lindley innovations based on the binomial thinning operator. The new model is particularly suitable for time series of counts exhibiting overdispersion and therefore c...

The existing bivariate integer-valued autoregressive process of order 1 (BINAR(1)) with negative binomial (NB) innovations is developed under stationary moment conditions and in particular under same level of over-dispersion index. In this paper, we propose a flexible BINAR(1) under NB innovations where the counting series are subject to two differ...

This article proposes a bivariate integer-valued autoregressive time-series model of order 1 (BINAR(1) with COM–Poisson marginals to analyze a pair of non stationary time series of counts. The interrelation between the series is induced by the correlated innovations, while the non stationarity is captured through a common set of time-dependent cova...

This paper proposes a generalized quasi-likelihood (GQL) function for estimating the vector of regression and over-dispersion effects for the respective series in the bivariate integer-valued autoregressive process of order 1 (BINAR(1)) with Negative Binomial (NB) marginals. The auto-covariance function in the proposed GQL is computed using some ‘r...

Bivariate counts are collected in many sectors of research but the analysis of such data is often challenging because each series of counts may exhibit different levels and types of dispersion. This paper addresses this problem by proposing a flexible bivariate COM-Poisson model that may handle any combination of over-, equi-and under-dispersion at...

This paper deals with the modeling of the first and second half number of football goals using a bivariate integer-valued first-order autoregressive model (BINAR(1)) with Negative Binomial (NB) innovations defined under timedependent moments. The main novelty of the paper is the estimation of the regression and over-dispersion parameters via a gene...

This paper proposes an unconstrained non-stationary BINMA(1) time series process with Poisson innovations under time-dependent moments where the cross-correlation structure is formed firstly by the jointly distributed innovations and secondly by relating the current variate observations with the previous-lagged innovation of the other series and vi...

This paper proposes a novel non-stationary BINMA time series model by extending two INMA processes where their innovation series follow the bivariate Poisson under time-varying moment assumptions. This paper also demonstrates, through simulation studies, the use and superiority of the generalized quasi-likelihood (GQL) approach to estimate the regr...

In recent years, Com–Poisson has emerged as one of the most popular discrete models in the analysis of count data owing to its flexibility in handling different types of dispersion. However, in a stationary longitudinal Com–Poisson count data set-up where the covariates are time independent, estimation of regression and dispersion parameters based...

Non-stationarity in bivariate time series of counts may be induced by a number of time-varying covariates affecting the bivariate responses due to which the innovation terms of the individual series as well as the bivariate dependence structure becomes non-stationary. So far, in the existing models, the innovation terms of individual INAR(1) series...

We investigate a new bivariate-integer valued moving average time series process where the innovation series follow the bivariate Poisson assumption under stationary moments and constant cross-correlations. Furthermore, due to the complication involved in specifying the joint likelihood function, this paper considers a robust generalized quasi-like...

Arsenal Football Club has been among the top four in the Premier League for long, but recently the club's performance has been quite inconsistent. This article performs a regression analysis to determine the factors that could explain these inconsistencies using a simple non-stationary first-order bivariate integer-valued autoregressive process wit...

In the last few years, the modelling of multivariate count data has been a topic of concern for many researchers in the field of epidemiology, agriculture, economics and finance. The most recent findings in the analysis of such data illustrate that it is easier to specify the likelihood function of these multivariate count responses through the use...

It is argued that the stock market development is an important ingredient for growth. As such this study tries to bring a small contribution by analysing the impact of stock market development on economic growth in Mauritius. A time series approach is conducted over the period of 1989 to 2011. Both the long run and short run relationship are analyz...

As more people are connected digitally, a highly automatic personal identification system is crucial. Dorsal hand vein biometric is an emerging biometric characteristic which is explored at its full swing. Although, researchers have deployed many hand biometrics using interesting techniques, it has not yet been accepted in many applications. Images...

It is of scientific interest to study the application of COM-Poisson model to the case of longitudinal response data, the analysis of which is quite challenging due to the fact that longitudinal responses of a subject are correlated and the correlation pattern is usually unknown. In this article, we extend the COM-Poisson GLM to the generalized lin...

Service quality in the banking sector is an important issue in an era where financial crisis is dominating the world economy. This paper assesses customer’s expectations and perceptions of service quality in the banking sector in Mauritius through the use of the Servqual questionnaire which was circulated among the customers of two major banks in M...

In our modern world, the intensive use of internet has imposed new lifestyles and encouraged new behaviour amongst many across the globe. With the development in Internet technologies, the emergence of online shopping has altered the way businesses operate. While many of them have embraced this platform to present their offerings, many customers on...

Hand vein biometrics is gaining popularity over other biometrics due to its uniqueness and stability. However, the variations of images at image capture process pose a challenge in the performance of a biometric security system. Different processing techniques applied so far on dorsal hand vein images cannot represent the different orientation of t...

It is of scientific interest to study the application of COM-Poisson model to the case of longitudinal response data, the analysis of which is quite challenging due to the fact that longitudinal responses of a subject are correlated and the correlation pattern is usually unknown. In this article, we extend the COM-Poisson GLM to the generalized lin...

Maximum-likelihood estimation technique is known to provide consistent and most efficient regression estimates but often this technique is tedious to implement, particularly in the modelling of correlated count responses. To overcome this limitation, researchers have developed semi- or quasi-likelihood functions that depend only on the correct spec...

No prior investigations have been made on the learning styles of students from different fields studying the same module at the University of Mauritius. Techniques have to be explored to depict their learning styles, which can lead to a more effective teaching. In this work, students from faculty of management and faculty of engineering studying on...

Internet banking offers many benefits but little research has been done about its acceptance in Mauritius. This paper aims at assessing the factors that contribute to the adoption of internet banking in Mauritius. To support our arguments, we use a logistic regression model based on a sample survey to analyze the factors that influence internet ban...

Lately, dorsal hand vein pattern is gaining popularity in biometric security system due to its uniqueness and stability. Though dorsal vein patterns are not complex, this does not reflect in its extraction and representation. Various existing methods consider vein pattern as straight lines or use some of its features like ending points and bifurcat...

Problem statement: The Maximum Likelihood Estimation (MLE) technique is the most efficient statistical approach to estimate parameters in a cross-sectional model. Often, MLE gives rise to a set of non-linear systems of equations that need to be solved iteratively using the Newton-Raphson technique. However, in some situations such as in the Negativ...