On Some Properties of Quasi-Negative-Binomial Distribution and Its Applications

The quasi-negative-binomial distribution was applied to queuing theory for determining the distribution of total number of customers served before the queue vanishes under certain assumptions. Some structural properties (probability generating function, convolution, mode and recurrence relation) for the moments of quasi-negative-binomial distribution are discussed. The distribution’s characterization and its relation with other distributions were investigated. A computer program was developed using R to obtain ML estimates and the distribution was fitted to some observed sets of data to test its goodness of fit

On Some Negative Integer Moments of Quasi-Negative-Binomial Distribution

Negative integer moments of the quasi-negative-binomial distribution (QNBD) are investigated. This distribution includes recurrence relations which are helpful in the solution of many applied statistical problems, particularly in life testing and survey sampling, where ratio estimators are useful. Results study show the negative-binomial distribution when the parameter θ2 is zero and also indicate the mean of the QNBD model when its parameters are changed

Classification of Arrhythmia by Using Deep Learning with 2-D ECG Spectral Image Representation

The electrocardiogram (ECG) is one of the most extensively employed signals used in the diagnosis and prediction of cardiovascular diseases (CVDs). The ECG signals can capture the heart's rhythmic irregularities, commonly known as arrhythmias. A careful study of ECG signals is crucial for precise diagnoses of patients' acute and chronic heart conditions. In this study, we propose a two-dimensional (2-D) convolutional neural network (CNN) model for the classification of ECG signals into eight classes; namely, normal beat, premature ventricular contraction beat, paced beat, right bundle branch block beat, left bundle branch block beat, atrial premature contraction beat, ventricular flutter wave beat, and ventricular escape beat. The one-dimensional ECG time series signals are transformed into 2-D spectrograms through short-time Fourier transform. The 2-D CNN model consisting of four convolutional layers and four pooling layers is designed for extracting robust features from the input spectrograms. Our proposed methodology is evaluated on a publicly available MIT-BIH arrhythmia dataset. We achieved a state-of-the-art average classification accuracy of 99.11\%, which is better than those of recently reported results in classifying similar types of arrhythmias. The performance is significant in other indices as well, including sensitivity and specificity, which indicates the success of the proposed method.Comment: 14 pages, 5 figures, accepted for future publication in Remote Sensing MDPI Journa

Economic Convergence in Context of Knowledge Economies in Asia: Instrumental Variable Estimation

Traditional convergence empirics overlook the role of knowledge as a contributor to economic convergence. This paper incorporates knowledge as a factor contributing towards economic convergence in Asian countries. In addition to knowledge, capital formation, interaction effects of tertiary education with ICT and knowledge and finally electricity consumption are also used in the said regression. Instrumental Variables estimation is used to test convergence hypothesis for sample Asian countries for data of time period 2001-2010. Empirical results are in favor of knowledge-augmented convergence, inferring that knowledge participates in convergence process across sample Asian countries. Factors like capital accumulation and interaction effects of ICT and knowledge with human capital and electricity consumption show their positive role in contributing to income per capita. Recommendations are made to improve the tertiary education sector and to promote economically productive research for advancing towards economic convergence in Asian region in particular and for UDCs in general

On Some Properties and Estimation of Size-Biased Polya-Eggenberger Distribution

A size-biased version of Polya-Eggenberger distribution is introduced explicitly and by a mixture model. The proposed distribution is unimodal with positive integer moments. The recurrence relation between moments (about the origin) of the proposed distribution is established and its relationship with other distributions is discussed. Different estimation techniques are proposed to estimate the parameters of the distribution

Correlation Between the Number of Epileptic and Healthy Children in Family Size that Follows a Size-Biased Modified Power Series Distribution

An expression for the correlation between the random number of epileptic and healthy children in family whose size follows a size-biased Modified Power Series Distribution (SBMPSD) is obtained and illustrated. As special cases, results are extracted for size biased Modified Negative Binomial Distribution (SBGNBD), size biased Modified Poisson Distribution (SBGPD) and size biased Modified Logarithmic Series Distribution (SBGLSD)

Negative Binomial Quasi Akash Distribution and its Applications

In this paper, we obtained a new model for count data by compounding of negative binomial with quasi Akash distribution. Important mathematical and statistical properties of the distribution have been derived and discussed. Then, parameter estimation is discussed using maximum likelihood method of estimation. Finally, the potential of the proposed model has been tested by chi-square goodness of fit test by modeling the real count data set