In this paper, we introduce a family of bivariate generalized Gompertz-power series distributions. This new class of bivariate distributions contains several models such as: bivariate generalized Gompertz -geometric, -Poisson, - binomial, -logarithmic, -negative binomial and bivariate generalized exponental-power series distributions as special cases. We express the method of construction and derive different properties of the proposed class of distributions. The method of maximum likelihood and EM algorithm are used for estimating the model parameters. Finally, we illustrate the usefulness of the new distributions by means of application to real data sets.

In this paper, we introduce a new class of bivariate distributions by com-pounding the bivariate generalized exponential and power-series distributions. This new class contains the bivariate generalized exponential-Poisson, bivariate general-ized exponential-logarithmic, bivariate generalized exponential-binomial and bivari-ate generalized exponential-negative binomial distributions as special cases. We derive different properties of the proposed class of distributions. It is observed that the pro-posed class of bivariate distributions is a very flexible class of distribution functions. The joint probability density functions can have a variety of shapes. It can be bimodal as well as heavy tailed also. This distribution has five parameters. The maximum likelihood estimators of the parameters cannot be obtained in closed form. We propose to use EM algorithm to compute the maximum likelihood estimators of the unknown parameters. It is observed that the proposed EM algorithm can be implemented very easily in practice. One data-set has been analyzed for illustrative purposes. It is ob-served that the proposed model and the EM algorithm work quite well in practice.

In this paper, a novel risk-based, two-objective (technical and economical) optimal reactive power dispatch method in a wind-integrated power system is proposed which is more consistent with operational criteria.  The technical objective includes the minimization of the new voltage instability risk index. The economical objective includes cost minimization of reactive power generation and active power loss. The proposed voltage instability risk employs a hybrid possibilistic (Delphi-Fuzzy)-probabilistic approach that takes into consideration the operator’s experience, the wind speed and demand forecast uncertainties when quantifying the risk index. The decision variables are the reactive power resources of the system. To solve the problem, the modified multi-objective particle swarm optimization algorithm with sine and cosine acceleration coefficients is utilized. The method is implemented on the modified IEEE 30-bus system. The proposed method is compared with those in the previously published literature, and the results confirm that the proposed risk index is better at estimating the voltage instability risk of the system, especially in cases with severe impact and low probability. In addition, according to the simulation results compared to typical security-based planning, the proposed risk-based planning may increase the security and economy of the system due to better utilization of system resources.

Many recent probability distributions are introduced by compounding the well-known continuous distributions  with the power series distribution.   In this paper, we provide a general closed-form expression  for the cumulative distribution function of this class. Then, we introduce  a new four parameter lifetime distribution called  Zhang-power series (ZPS) distribution. This distribution is very useful in the lifetime, reliability and extreme-value data analysis. The distribution properties including survival function, hazard function and limiting behavior of the probability density  and hazard functions are studied. The method of maximum likelihood estimation is used to estimate the model parameters. Applications to real data sets are given to show the flexibility and potentiality of the proposed model.

A new generalized distribution called the gamma odd power generalized Weibull-G family of distributions is developed and studied. Some special models of the new family of distribution are explored. Statistical properties of the new family of distributions including the quantile function, ordinary and incomplete moments, probability weighted moments, stochastic ordering, distribution of the order statistics, and Ré, nyi entropy are presented. The maximum likelihood method is used for estimating model parameters, and Monte Carlo simulation is conducted to examine the performance of the model. The flexibility of the new family of distributions is demonstrated by means of two applications to real data sets.

A new generalized family of distributions called the odd power generalized Weibull-G family of distributions is developed. Some properties of the new family of distributions including quantile function, moments, incomplete and probability weighted moments, distribution of the order statistics and Ré, nyi entropy are derived. Estimation of model parameters using maximum likelihood estimation technique and simulation study to examine the bias and mean square error are discussed. Applications to real data sets to illustrate the applicability of the generalized family of distributions is also given.

Visible Light Communication (VLC) has emerged as a powerful technique for wireless communication systems. Providing high data rate and increasing capacity are the major problems in VLC. Recent evidence suggests that Multiple Input Multiple Output (MIMO) technique can offers improved data rates and increased link range. This paper describes the design and implementation of visible light communication system in indoor environment exploring the benefits of MIMO. The specific objective of this research was to implement a 4×4 Multiple Input (LEDs) Multiple Output (photodetectors)-VLC communication system, where a 16 white power LEDs in four arrays are setting up at transmitter and four RX modules are setting up at receiver side without the need for additional power or bandwidth as well as analyze a mathematical model for a VLC-×4 MIMO with different modes such as the suitable angles to cover the entire room. The research designs practically an electronic circuit for the transmitter and receiver with inexpensive components. The power distribution of different propagation modes is calculated for Single Input Single Output (SISO) and MIMO channels in typical room dimensions. The results in this paper indicate that the power is distributed uniformly for entire room when implemented VLC-MIMO as compared to VLC-SISO. Furthermore, a 4×4 MIMO implementing VLC is compared in term of BER vs. SINR with SISO communication system for both Line of Sight (LOS) and Non Line of Sight (NLOS) propagation modes. Comparing the two results of LOS and NLOS, it can be seen that a 4×4 MIMO implementing VLC for LOS perform better than the same system with NLOS due to decreasing in the received power resulted from the multipath effect.

In this paper, we introduce a novel family of statistical models called a new alpha power type-1 family of distributions. Three sub-cases of the family are discussed. Based on the novel family, a special model, explicitly, a new alpha power type-1-Weibull distribution is studied in depth. The new model has very interesting patterns of failure rates like increasing, decreasing, bathtub, and parabola-down. Hence, it is so flexible. Based on the comparison analysis, among five well-known models, it has an impact on health data analysis. Furthermore, the count data models capable of handling overdispersion and zero-inflation are discussed and applied the real health data. The zero-inflated negative binomial model in the frequentist approach has shown its popularity in handling both overdispersion and zero-inflation simultaneously, while the discrete Weibull model with the logit(q) link in the Bayesian approach outperformed its counterparts.