New Generalizations of Exponential Distribution with Applications

The main purpose of this paper is to present k-Generalized Exponential Distribution which among other things includes Generalized Exponential and Weibull Distributions as special cases. Besides, we also obtain three-parameter extension of Generalized Exponential Distribution. We shall also discuss moment generating functions (MGFs) of these newly introduced distributions

Modelling the number of olive groves in Spanish municipalities

The univariate generalized Waring distribution (UGWD) is presented as a new model to describe the goodness of fit, applicable in the context of agriculture. In this paper, it was used to model the number of olive groves recorded in Spain in the 8,091 municipalities recorded in the 2009 Agricultural Census, according to which the production of oil olives accounted for 94% of total output, while that of table olives represented 6% (with an average of 44.84 and 4.06 holdings per Spanish municipality, respectively). UGWD is suitable for fitting this type of discrete data, with strong left-sided asymmetry. This novel use of UGWD can provide the foundation for future research in agriculture, with the advantage over other discrete distributions that enables the analyst to split the variance. After defining the distribution, we analysed various methods for fitting the parameters associated with it, namely estimation by maximum likelihood, estimation by the method of moments and a variant of the latter, estimation by the method of frequencies and moments. For oil olives, the chi-square goodness of fit test gives p-values of 0.9992, 0.9967 and 0.9977, respectively. However, a poor fit was obtained for the table olive distribution. Finally, the variance was split, following Irwin, into three components related to random factors, external factors and internal differences. For the distribution of the number of olive grove holdings, this splitting showed that random and external factors only account about 0.22% and 0.05%. Therefore, internal differences within municipalities play an important role in determining total variability

Modelling the number of olive groves in Spanish municipalities

The univariate generalized Waring distribution (UGWD) is presented as a new model to describe the goodness of fit, applicable in the context of agriculture. In this paper, it was used to model the number of olive groves recorded in Spain in the 8,091 municipalities recorded in the 2009 Agricultural Census, according to which the production of oil olives accounted for 94% of total output, while that of table olives represented 6% (with an average of 44.84 and 4.06 holdings per Spanish municipality, respectively). UGWD is suitable for fitting this type of discrete data, with strong left-sided asymmetry. This novel use of UGWD can provide the foundation for future research in agriculture, with the advantage over other discrete distributions that enables the analyst to split the variance. After defining the distribution, we analysed various methods for fitting the parameters associated with it, namely estimation by maximum likelihood, estimation by the method of moments and a variant of the latter, estimation by the method of frequencies and moments. For oil olives, the chi-square goodness of fit test gives p-values of 0.9992, 0.9967 and 0.9977, respectively. However, a poor fit was obtained for the table olive distribution. Finally, the variance was split, following Irwin, into three components related to random factors, external factors and internal differences. For the distribution of the number of olive grove holdings, this splitting showed that random and external factors only account about 0.22% and 0.05%. Therefore, internal differences within municipalities play an important role in determining total variability.This research is financed by Vice-Rector’s Office for Political Science and Research-University of Granada, through the project “Social-Labour Statistics and Demography” (30.BB.11.1101) at the Faculty of Labour Sciences

Uses of the Hypergeometric Distribution for Determining Survival or Complete Representation of Subpopulations in Sequential Sampling

This thesis will explore the hypergeometric probability distribution by looking at many different aspects of the distribution. These include, and are not limited to: history and origin, derivation and elementary applications, properties, relationships to other probability models, kindred hypergeometric distributions and elements of statistical inference associated with the hypergeometric distribution. Once the above are established, an investigation into and furthering of work done by Walton (1986) and Charlambides (2005) will be done. Here, we apply the hypergeometric distribution to sequential sampling in order to determine a surviving subcategory as well as study the problem of and complete representation of the subcategories within the population

Software Reliability models for the first stage of Software Projects

A software reliability analysis for the first stage of software projects is presented. At this very first stage of testing we expect an increasing failure rate, where the usual software reliability growth models based on non homogeneous Poisson processes like the Goel-Okumoto or Musa-Okumoto can not be applied. However, our analysis involves some models that combine reliability growth with increasing failure rates like the logistic and delayed S-shaped models. Our analysis also includes a new model based on contagion as in the increasing failure rate as in the reliability growth stages. We point out that increasing failure rate stages are important to be modeled since corrective actions can be taken soon and also that this characteristics highlights under modern development methodologies which development is performed simultaneously as testing, like in Agile and TDD (Test driven development). Results of the application of those models to real datasets is shown.Sociedad Argentina de Informática e Investigación Operativ

Software Reliability models for the first stage of Software Projects

A software reliability analysis for the first stage of software projects is presented. At this very first stage of testing we expect an increasing failure rate, where the usual software reliability growth models based on non homogeneous Poisson processes like the Goel-Okumoto or Musa-Okumoto can not be applied. However, our analysis involves some models that combine reliability growth with increasing failure rates like the logistic and delayed S-shaped models. Our analysis also includes a new model based on contagion as in the increasing failure rate as in the reliability growth stages. We point out that increasing failure rate stages are important to be modeled since corrective actions can be taken soon and also that this characteristics highlights under modern development methodologies which development is performed simultaneously as testing, like in Agile and TDD (Test driven development). Results of the application of those models to real datasets is shown.Sociedad Argentina de Informática e Investigación Operativ