An alternative hyper-Poisson integer-valued GARCH model with application to polio, internet protocol and COVID-19 data

Time series of counts are observed widely in actuarial science, finance, epidemiology and biology. These time series may exhibit over-, equi- and under-dispersion. The Poisson distribution is commonly used in count time series models, but it is restricted by the equality of mean and variance. Other distributions such as the generalized Poisson, double Poisson, hyper-Poisson, and COM-Poisson distributions have been proposed to replace the Poisson distribution to model the different levels of dispersion in time series of counts. These models have certain limitations such as complex expressions for the mean and variance which complicate the formulation as GARCH models. In this study, we propose an alternative hyper-Poisson (AHP) distribution, with simple forms of conditional mean and variance, for an integer-valued GARCH (INGARCH) model for time series of counts that also exhibit the different levels of dispersion. We demonstrate that the AHP-INGARCH model is comparable to some existing INGARCH models. Additionally, the model can cover a wider range of dispersion. The maximum likelihood estimation can be used to estimate the parameters of the proposed model. Applications to three real-life data sets related to polio, internet protocol and daily COVID-19 new deaths underscore the usefulness of the proposed model in studying both over-dispersed and under-dispersed time series of counts

Accutome PachPen handheld ultrasonic pachymeter: intraobserver repeatability and interobserver reproducibility by personnel of different training grades

Abstract To assess the intra-observer repeatability and inter-observer reproducibility of central corneal thickness (CCT) measurements of PachPen (Accutome, Inc., Pennsylvania, USA), a hand-held, portable ultrasonic pachymeter when used by an ophthalmic nurse compared to an ophthalmologist. Ophthalmology Clinic, University of Malaya Medical Center In this prospective study, CCT was measured in 184 eyes of 92 healthy subjects, first by a corneal surgeon experienced in ultrasound pachymetry (Observer 1) followed by an ophthalmic nurse new to the procedure (Observer 2). Nine measurements were obtained from each eye by each observer, independently. Measurements were compared between the observers. Coefficients of repeatability and reproducibility were calculated. The Bland-Altman plot was used to assess agreement between observers. Mean age of the study population was 54.3 ± 15.2 years old and consisted of 43.5 % male. Mean CCT as measured by Observers 1 and 2 were 528.3 ± 32.9 and 530.7 ± 33.3 lm, respectively. Observer 1 showed higher repeatability of measurements compared to that of Observer 2 (coefficient of repeatability 3.46 vs. 5.55 %). The measurements by both observers showed high correlation (0.96) and good agreement (mean difference -2.4 lm; 95 % limits of agreement -21.4, 16.7 lm). Coefficient of reproducibility of measurements between observers was 5.08 %. Accutome PachPen hand-held ultrasound pachymeters gives excellent intra-observer repeatability and inter-observer reproducibility by personnel of different training grades

Accutome PachPen handheld ultrasonic pachymeter: intraobserver repeatability and interobserver reproducibility by personnel of different training grades

Abstract To assess the intra-observer repeatability and inter-observer reproducibility of central corneal thickness (CCT) measurements of PachPen (Accutome, Inc., Pennsylvania, USA), a hand-held, portable ultrasonic pachymeter when used by an ophthalmic nurse compared to an ophthalmologist. Ophthalmology Clinic, University of Malaya Medical Center In this prospective study, CCT was measured in 184 eyes of 92 healthy subjects, first by a corneal surgeon experienced in ultrasound pachymetry (Observer 1) followed by an ophthalmic nurse new to the procedure (Observer 2). Nine measurements were obtained from each eye by each observer, independently. Measurements were compared between the observers. Coefficients of repeatability and reproducibility were calculated. The Bland-Altman plot was used to assess agreement between observers. Mean age of the study population was 54.3 ± 15.2 years old and consisted of 43.5 % male. Mean CCT as measured by Observers 1 and 2 were 528.3 ± 32.9 and 530.7 ± 33.3 lm, respectively. Observer 1 showed higher repeatability of measurements compared to that of Observer 2 (coefficient of repeatability 3.46 vs. 5.55 %). The measurements by both observers showed high correlation (0.96) and good agreement (mean difference -2.4 lm; 95 % limits of agreement -21.4, 16.7 lm). Coefficient of reproducibility of measurements between observers was 5.08 %. Accutome PachPen hand-held ultrasound pachymeters gives excellent intra-observer repeatability and inter-observer reproducibility by personnel of different training grades

A class of bivariate negative binomial distributions with different index parameters in the marginals Keywords and Phrases: Extension of trivariate reduction Meixner class of polynomials and Srivastava's triple hypergeometric series Canonical expansions a

a b s t r a c t In this paper, we consider a new class of bivariate negative binomial distributions having marginal distributions with different index parameters. This feature is useful in statistical modelling and simulation studies, where different marginal distributions and a specified correlation are required. This feature also makes it more flexible than the existing bivariate generalizations of the negative binomial distribution, which have a common index parameter in the marginal distributions. Various interesting properties, such as canonical expansions and quadrant dependence, are obtained. Potential application of the proposed class of bivariate negative binomial distributions, as a bivariate mixed Poisson distribution, and computer generation of samples are examined. Numerical examples as well as goodnessof-fit to simulated and real data are also given here in order to illustrate the application of this family of bivariate negative binomial distributions

Parameter estimation by minimizing a probability generating function-based power divergence

Generating function-based statistical inference is an attractive approach if the probability (density) function is complicated when compared with the generating function. Here, we propose a parameter estimation method that minimizes a probability generating function (pgf)-based power divergence with a tuning parameter to mitigate the impact of data contamination. The proposed estimator is linked to the M-estimators and hence possesses the properties of consistency and asymptotic normality. In terms of parameter biases and mean squared errors from simulations, the proposed estimation method performs better for smaller value of the tuning parameter as data contamination percentage increases. © 2018, © 2018 Taylor & Francis Group, LLC

Some Probabilistic Generalizations of the Cheney–Sharma and Bernstein Approximation Operators

The objective of this paper is to give some probabilistic derivations of the Cheney, Sharma, and Bernstein approximation operators. Motivated by these probabilistic derivations, generalizations of the Cheney, Sharma, and Bernstein operators are defined. The convergence property of the Bernstein generalization is established. It is also shown that the Cheney–Sharma operator is the Szász–Mirakyan operator averaged by a certain probability distribution

Epidemiology of human leptospirosis in Malaysia, 2004–2012

Leptospirosis is an emerging disease, especially in countries with a tropical climate such as Malaysia. A dramatic increase in the number of cases has been reported over the last decade; however, information on the epidemiological trends of this disease is lacking. The objective of this study is to provide an epidemiological description of human leptospirosis cases over a 9-year period (2004–2012) and disease relationship with meteorological, geographical, and demographical information.A retrospective study was undertaken to describe the patterns of human leptospirosis cases and their association with intrinsic (sex, age, and ethnicity) and extrinsic (location, rainfall, and temperature)factors. Data was grouped according to age, sex, ethnicity, seasonality and geographical distribution,and analyzed using statistical tools to understand the influence of all the different factors on disease incidence. A total of 12,325 cases of leptospirosis were reported between 2004 and 2012 with an upward trend in disease incidence, with the highest in 2012. Three hundred thirty-eight deaths were reported with an overall case fatality rate of 2.74%, with higher incidence in males (9696; 78.7%) compared with female patients (2629; 21.3%), and overall male to female ratio of 3.69:1. Patients aged cohorts between 30–39years old (16.22 per 100,000 population) had the highest disease incidence while the lowest incidence occurred between \u3c1 to 9 years old (3.44 per 100,000 population). The average incidence was highest amongst Malays (10.97 per 100,000 population), followed by Indians (7.95 per 100,000 population). Stratification according to geographical distribution showed that the state of Malacca had the highest average disease incidence (11.12 per 100,000 population) followed by Pahang (10.08 per 100,000 population). The states of Terengganu, Kelantan, and Perak recorded similar rates of incidence (≈8.00 per 100,000population), while Johor with the least number of reported cases (1.80 per 100,000 population). Positive relationships were recorded between the number of reported cases with the number of raining days per month and monthly average temperature (p-value \u3c 0.05). However, no significant association was noted between rainfall volume and number of reported Leptospirosis cases.This collaborative efforts between medical, academic and governmental institutions has enabled the construction of this comprehensive database that is essential to understand the disease trends in Malaysia and add insights into the prevention and control of this disease