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In this article we study a subfamily of the slashed-Weibull family. This subfamily can be seen as an extension of the Rayleigh distribution with more flexibility in terms of the kurtosis of distribution. This special feature makes the extension suitable for fitting atypical observations. It arises as the ratio of two independent random variables, the one in the numerator being a Rayleigh distribution and a power of the uniform distribution in the denominator. We study some probability properties, discuss maximum likelihood estimation and present real data applications indicating that the slashed-Rayleigh distribution can improve the ordinary Rayleigh distribution in fitting real data.

The best management practices for cover cropping in citrus orchards, particularly in terms of species selection and termination methods, remain unclear. This study assessed the short-term effects of different cover crop species (vetch, medics and oats) and termination methods (slashed vs. non-slashed) on soil pH and enzyme activities (β-glucosidase, acid phosphatase, and urease) in a citrus orchard with sandy soil. A randomized complete block design with a factorial treatment structure and six replications was used. Soil samples were collected before and one year after cover crop establishment. The results showed that cover cropping increased soil pH from 5.42 to 6.00 after one year. However, no statistically significant differences were observed in soil pH or enzyme activities among cover crop species or termination methods. Marginal increases in enzyme activities were observed under leguminous cover crops, and these changes were insufficient to indicate strong treatment effects. Correlation and principal component analyses revealed that soil enzyme activities were more strongly influenced by soil properties (depth, carbon content and moisture) than by cover crop species or termination methods. These findings suggest that, under sandy soil conditions and within a one-year period, cover cropping has limited immediate effects on soil biological indicators in citrus orchards. Longer-term studies are recommended to assess cumulative impacts.

In this article, the slashed Lomax distribution is introduced, which is an asymmetric distribution and can be used for fitting thick-tailed datasets. Various properties are explored, such as the density function, hazard rate function, Renyi entropy, r-th moments, and the coefficients of the skewness and kurtosis. Some useful characterizations of this distribution are obtained. Furthermore, we study a slashed Lomax regression model and the expectation conditional maximization (ECM) algorithm to estimate the model parameters. Simulation studies are conducted to evaluate the performances of the proposed method. Finally, two sets of data are applied to verify the importance of the slashed Lomax distribution.

Specifying a proper statistical model to represent asymmetric lifetime data with high kurtosis is an open problem. In this paper, the three-parameter, modified, slashed, generalized Rayleigh family of distributions is proposed. Its structural properties are studied: stochastic representation, probability density function, hazard rate function, moments and estimation of parameters via maximum likelihood methods. As merits of our proposal, we highlight as particular cases a plethora of lifetime models, such as Rayleigh, Maxwell, half-normal and chi-square, among others, which are able to accommodate heavy tails. A simulation study and applications to real data sets are included to illustrate the use of our results.

In this paper, the scale mixture of Rayleigh (SMR) distribution is introduced. It is proven that this new model, initially defined as the quotient of two independent random variables, can be expressed as a scale mixture of a Rayleigh and a particular Generalized Gamma distribution. Closed expressions are obtained for its pdf, cdf, moments, asymmetry and kurtosis coefficients. Its lifetime analysis, properties and Rényi entropy are studied. Inference based on moments and maximum likelihood (ML) is proposed. An Expectation-Maximization (EM) algorithm is implemented to estimate the parameters via ML. This algorithm is also used in a simulation study, which illustrates the good performance of our proposal. Two real datasets are considered in which it is shown that the SMR model provides a good fit and it is more flexible, especially as for kurtosis, than other competitor models, such as the slashed Rayleigh distribution.

In this paper we introduce a new distribution constructed on the basis of the quotient of two independent random variables whose distributions are the half-normal distribution and a power of the exponential distribution with parameter 2 respectively. The result is a distribution with greater kurtosis than the well known half-normal and slashed half-normal distributions. We studied the general density function of this distribution, with some of its properties, moments, and its coefficients of asymmetry and kurtosis. We developed the expectation–maximization algorithm and present a simulation study. We calculated the moment and maximum likelihood estimators and present three illustrations in real data sets to show the flexibility of the new model.

In this paper we introduce a new distribution, namely, the slashed half-normal distribution and it can be seen as an extension of the half-normal distribution. It is shown that the resulting distribution has more kurtosis than the ordinary half-normal distribution. Moments and some properties are derived for the new distribution. Moment estimators and maximum likelihood estimators can computed using numerical procedures. Results of two real data application are reported where model fitting is implemented by using maximum likelihood estimation. The applications illustrate the better performance of the new distribution.

In this paper we propose an extension of the generalized half-normal distribution studied in Cooray and Ananda (Commun Stat 37:1323–1337, 2008 ). This new distribution is defined by considering the quotient of two random variables, the one in the numerator being a generalized half normal distribution and the one in the denominator being a power of the uniform distribution on ( 0 , 1 ) , respectively. The resulting distribution has greater kurtosis than the generalized half normal distribution. The density function of this more general distribution is derived jointly with some of its properties and moments. We discuss stochastic representation, maximum likelihood and moments estimation. Applications to real data sets are reported revealing that the proposed distribution can fit real data better than the slashed half-normal, generalized half-normal and Birnbaum–Saunders distributions.