ABSTRACT
The exponentiated generalized Gull alpha power exponential distribution is an extension of the exponential distribution that can model data characterized by various shapes of the hazard function. However, change point problem has not been studied for this distribution. In this study, the change point detection of the parameters of the exponentiated generalized Gull alpha power exponential distribution is studied using the modified information criterion. In addition, the binary segmentation procedure is used to identify multiple change point locations. The assumption is that all the parameters of the EGGAPE distributions are considered changeable. Simulation study is conducted to illustrate the power of the modified information criterion in detecting change point in the parameters with different sample sizes. Three applications related to COVID-19 data are used to demonstrate the applicability of the MIC in detecting change point in real life scenario.
ABSTRACT
An infinite-server queueing model with state-dependent arrival process and exponential distribution of service time is analyzed. It is assumed that the difference between the value of the arrival rate and total service rate becomes positive starting from a certain value of the number of customers in the system. In this paper, time until reaching this value by the number of customers in the system is called the pseudo steady-state period (PSSP). Distribution of duration of PSSP, its raw moments and its simple approximation under a certain scaling of the number of customers in the system are analyzed. Novelty of the considered problem consists of an arbitrary dependence of the rate of customer arrival on the current number of customers in the system and analysis of time until reaching from below a certain level by the number of customers in the system. The relevant existing papers focus on the analysis of time interval since exceeding a certain level until the number of customers goes down to this level (congestion period). Our main contribution consists of the derivation of a simple approximation of the considered time distribution by the exponential distribution. Numerical examples are presented, which confirm good quality of the proposed approximation.
ABSTRACT
In this paper, the main aim is to define a statistical distribution that can be used to model COVID-19 data in Mexico and Canada. Using the method of exponentiation on the gull alpha exponential distribution introduces a new distribution with three parameters called the exponentiated gull alpha power exponential (EGAPE) distribution. The distribution has the benefit of being able to represent monotonic and nonmonotonic failure rates, both of which are often seen in dependability issues. It is possible to determine the quantile function as well as the skewness, kurtosis, and order statistics of the suggested distribution. The approach of maximum likelihood is used in order to calculate the parameters of the model, and the RMSE and average bias are utilised in order to evaluate how successful the strategy is. In conclusion, the flexibility of the new distribution is demonstrated by modeling COVID-19 data. From the practical application, we can conclude that the proposed model outperformed the competing models and therefore can be used as a better option for modeling COVID-19 and other related datasets.
ABSTRACT
In this article, we use exponentiated exponential distribution as a suitable statistical lifetime model for novel corona virus (covid-19) Kerala patient data. The suitability of the model has been followed by different statistical tools like the value of logarithm of likelihood, Kolmogorov–Smirnov distance, Akaike information criterion, Bayesian information criterion. Moreover, likelihood ratio test and empirical posterior probability analysis are performed to show its suitability. The maximum-likelihood and asymptotic confidence intervals for the parameters are derived from Fisher information matrix. We use the Markov Chain Monte Carlo technique to generate samples from the posterior density function. Based on generated samples, we can compute the Bayes estimates of the unknown parameters and can also construct highest posterior density credible intervals. Further we discuss the Bayesian prediction for future observation based on the observed sample. The Gibbs sampling technique has been used for estimating the posterior predictive density and also for constructing predictive intervals of the order statistics from the future sample.
ABSTRACT
This paper aims to introduce a superior discrete statistical model for the coronavirus disease 2019 (COVID-19) mortality numbers in Saudi Arabia and Latvia. We introduced an optimal and superior statistical model to provide optimal modeling for the death numbers due to the COVID-19 infections. This new statistical model possesses three parameters. This model is formulated by combining both the exponential distribution and extended odd Weibull family to formulate the discrete extended odd Weibull exponential (DEOWE) distribution. We introduced some of statistical properties for the new distribution, such as linear representation and quantile function. The maximum likelihood estimation (MLE) method is applied to estimate the unknown parameters of the DEOWE distribution. Also, we have used three datasets as an application on the COVID-19 mortality data in Saudi Arabia and Latvia. These three real data examples were used for introducing the importance of our distribution for fitting and modeling this kind of discrete data. Also, we provide a graphical plot for the data to ensure our results.