Academic literature on the topic 'SBG Model Beta distribution Beta geometric Beta binomial'

In the competitive mobile gaming industry, retaining players and maximizing engagement are critical for sustained success. This study employs the Beta-Geometric/Negative Binomial Distribution (BG/NBD) model to predict customer lifetime value (CLTV) and identify players at risk of churning. By targeting these high-risk players with tailored marketing strategies, gaming companies can significantly improve retention rates and overall player engagement.

The current research offers an enhanced three-parameter lifetime model that combines the unit Burr XII distribution with a power series distribution. The novel class of distribution is named the unit Burr XII power series (UBXIIPS). This compounding technique allows for the production of flexible distributions with strong physical meanings in domains such as biology and engineering. The UBXIIPS class includes the unit Burr XII Poisson (UBXIIP) distribution, the unit Burr XII binomial distribution, the unit Burr XII geometric distribution, and the unit Burr XII negative binomial distribution. The statistical properties of the class include formulas for the density and cumulative distribution functions, and limiting behaviour, moments and incomplete moments, entropy measures, and quantile function are provided. For estimating population parameters and fuzzy reliability for the UBXIIP model, maximum likelihood and Bayesian approaches are studied by the Metropolis–Hastings algorithm. For maximum likelihood estimators, the length of asymptotic confidence intervals is specified, whereas, for Bayesian estimators, the length of credible confidence intervals is assigned. A simulation investigation of the UBXIIP model was established to evaluate the performance of suggested estimates. In addition, the UBXIIP distribution is explored using real-world data. The UBXIIP distribution appears to offer some benefits in understanding lifetime data when compared to unit Weibull, beta, Kumaraswamy, Kumaraswamy Kumaraswamy, Marshall-Olkin Kumaraswamy, and Topp–Leone Weibull Lomax distributions.

Many businesses follow the repeat operation of a particular customer with a same store in different discrete time point. Customer retention comprises the probability of customer that alive in particular store in different purchase occasion. Different purchase occasion with a particular store occur at regular time intervals. The main goal of this paper is to predict future purchase patterns for rural and urban customer that can be described by the structural characteristics. The discrete time beta geometric model allows to heterogeneity of each of rural and urban customer behavioral process. The model is applied in 194 household from urban and 196 household from rural. Each household visited three times once in every three months. The study reveals that customer retention of rural customer is more than the urban customer.

Introduction: Little attention has been paid to modeling count data with the geometric distribution. There are many real-life phenomena with a constant probability of first success. However, in practice, the probability of the first success may vary, making simple geometric models unsuitable for modeling such data. One can assume one of many continuous distributions for modeling the probability of first success with the parameter space [0, 1]. In this respect Beta distribution defined on the standard unit interval [0,1] is the most useful distribution due to its ability to accommodate a wide range of shapes. Thus, in this paper, by mixing Beta and geometric distribution, we developed a Beta-geometric distribution for modeling the count data through application to real-life count data on time to the first antenatal care (ANC) visit.
 Methods: The estimation of the distribution parameters using the method of moments, maximum likelihood estimation (MLE) method, and Bayesian estimation approach are provided. Based on the Beta-geometric distribution, we developed a new Beta-geometric regression model for analyzing count data that follow the geometric distribution. The goodness of fit of the derived model has been tested using real data on time to the first ANC visit.
 Results: Beta-geometric distribution has a simple form for its probability mass function (pmf), and is flexible in capturing both underdispersion and overdispersion that may present in count data. It was found that the proposed Beta-geometric regression model fit the count data on the first ANC visit better than simple geometric distribution or Negative Binomial distribution.
 Conclusion: Unlike the Poisson or Negative Binomial distribution, Beta-geometric distribution does not need an additional parameter to accommodate underdispersion or overdispersion and thus could be a flexible choice for analyzing any count data. The goodness of fit test of the Beta-geometric model provides better fitting of the model to real data on time to first ANC visit than geometric or Negative binomial models.

In this era of Internet, there are many lots of retailers in the e-commerce industry for whom the customers are assets. E-commerce means buying and selling the products through Internet in online mode. E-commerce established many employment opportunities to the people from anywhere because there is no direct interaction between the seller and the buyer. Many people are purchasing things using this e-commerce application. There are many e-commerce websites available for the customers. So the Retailers want to analyze their relationship with the customers so that they can produce or buy the goods according to their requirements. However, this work mainly focuses on predicting the customer lifetime value (CLV) using Beta-Geometric/Negative Binomial Distribution Model (BG\NBD) and Gamma-Gamma Model.