# Yuri A. Iriarte's research while affiliated with University of Antofagasta and other places

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## Publications (24)

In this paper, a modified exponentiated family of distributions is introduced. The new model was built from a continuous parent cumulative distribution function and depends on a shape parameter. Its most relevant characteristics have been obtained: the probability density function, quantile function, moments, stochastic ordering, Poisson mixture wi...

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, mome...

The beta and Kumaraswamy distributions are two of the most widely used distributions for modeling bounded data. When the histogram of a certain dataset exhibits increasing or decreasing behavior, one-parameter distributions such as the power, Marshall–Olkin extended uniform and skew-uniform distributions become viable alternatives. In this article,...

The generalized bimodal distribution is especially efficient in modeling univariate data exhibiting symmetry and bimodality. However, its performance is poor when the data show important levels of skewness. This article introduces a new unimodal/bimodal distribution capable of modeling different skewness levels. The proposal arises from the recentl...

In this article, we introduce a new probability distribution generator called the Lambert-F generator. For any continuous baseline distribution F, with positive support, the corresponding Lambert-F version is generated by using the new generator. The result is a new class of distributions with one extra parameter that generalizes the baseline distr...

This article introduces a new probability distribution capable of modeling positive data that present different levels of asymmetry and high levels of kurtosis. A slashed quasi-gamma random variable is defined as the quotient of independent random variables, a generalized gamma is the numerator, and a power of a standard uniform variable is the den...

In this paper, a general class of modified power-symmetric distributions is introduced. By choosing as symmetric model the normal distribution, the modified power-normal distribution is obtained. For the latter model, some of its more relevant statistical properties are examined. Parameters estimation is carried out by using the method of moments a...

This article proposes a new distribution, the Confluent hypergeometric slashed-Rayleigh distribution. The new distribution can be seen as an alternative to the slashed-Rayleigh distribution. It arises as quotient of two independent random variables, one being a Rayleigh distribution in the numerator the other a square root of the beta 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...

An extension of the generalized half-normal distribution, given by Cooray and Ananda [5], is proposed and studied. We use the quadratic rank transmutation map to generate a transmuted version of the generalized half-normal distribution. We study some probability properties, discuss maximum likelihood estimation and present real data application ind...

In this article, we introduce a new distribution for modeling positive data sets with high kurtosis, the modified slashed generalized exponential distribution. The new model can be seen as a modified version of the slashed generalized exponential distribution. It arises as a quotient of two independent random variables, one being a generalized expo...

In this paper, a new class of slash distribution is introduced. The distribution is obtained as a quotient of two independent random variables, specifically, a Lindley-Weibull distribution divided by a power of a uniform distribution. The new model can be considered as an extension of the Lindley-Weibull law more flexible in terms of the kurtosis o...

In this paper, the Rayleigh–Lindley (RL) distribution is introduced, obtained by compounding the Rayleigh and Lindley discrete distributions, where the compounding procedure follows an approach similar to the one previously studied by Adamidis and Loukas in some other contexts. The resulting distribution is a two-parameter model, which is competiti...

In this article, we introduce the slashed power-Lindley distribution. This model can be seen as an extension of the power-Lindley distribution with more flexibility in terms of the kurtosis of distribution. It arises as the ratio of two independent random variables, the one being a power-Lindley distribution and a power of the uniform distribution....

The problem of estimating the ratio of coefficients of variation of two independent lognormal populations is considered. We propose two closed-form approximate confidence intervals (CIs), one is based on the method of variance estimate recovery (MOVER), and another is based on the fiducial approach. The proposed CIs are compared with another CI ava...

A new family of slash distributions, the modified slashed-Rayleigh distribution, is proposed and studied. This family is an extension of the ordinary Rayleigh distribution, being more flexible in term of distributional kurtosis. Its arises as the quotient of two independent random variable, one being a Rayleigh distribution in the numerator and a p...

A new univariate three-parameter distribution, the transmuted exponentiated Maxwell distribution, is proposed and studied. This new univariate distribution can be seen as generalization of the Maxwell distribution and its respective exponentiated and transmuted versions. The new generalization is generate using the families of exponentiated and tra...

A new two-parameter distribution, the gamma-Maxwell distribution, is proposed and studied. We generate the new distribution using the gamma-G generator of distributions proposed by Zografos and Balakrishnan (200915.
Zografos K, Balakrishnan N (2009) On families of beta- and generalized gamma-generated distributions and associated inference, Stat. M...

We introduce a new family of distributions suitable for fitting positive data sets with high kurtosis which is called the Slashed Generalized Rayleigh Distribution. This distribution arises as the quotient of two independent random variables, one being a generalized Rayleigh distribution in the numerator and a power of the uniform distribution in t...

In this paper we introduce a new distribution for modeling positive data with high kurtosis. This distribution can be seen as an extension of the exponentiated Rayleigh distribution. This extension builds on the quotient of two independent random variables, one exponentiated Rayleigh in the numerator and Beta(q,1) in the denominator with q>0. It is...

Statistical analysis procedures's quality depends on the proper use of the probability distributions. For that reason, many probability distributions have been generalized. For example, Vodă in [13] introduced the generalized Rayleigh distribution, a model widely used in reliability analysis. In this article, we introduce an extension of the genera...

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, t...

In this paper we introduce an extension of the Maxwell probability distribution. This extension is generated using the quadratic rank transmutation map studied by Shaw and Buckley in [13], considering as the basis function the cumulative distribution function of the Maxwell model. We study probabilistic properties, we perform statistical inference...

## Citations

... By applying the method proposed in Barranco-Chamorro et al. [15], the convergence in law of the SPHN(σ, α, q) model, as q → ∞, to a PHN(σ, α) distribution is next established. To highlight the fact that we are taking the limit for q → ∞, the subindex q is used to refer to T q ∼ SPHN(σ, α, q). ...

... Then, a regression-based functional form through a link function is introduced. For example, models based on the arcsecant hyperbolic Weibull [5], Lambert-uniform [6], unit-Birnbaum-Saunders [7][8][9][10], unit-Burr-XII [11], exponentiated arcsecant hyperbolic normal [12], unit-Chen [13], logextended exponential-geometric [14], Johnson-t [15], power Johnson SB [16], L-logistic [17], unit-Weibull [18][19][20], generalized Johnson SB [21], and Kumaraswamy [22] distributions have been postulated. These formulations have been proposed to model the conditional quantiles of a bounded response variable and are well known in the literature [23]. ...

... Other practical examples of bimodality in data can be seen in [4][5][6]. In the literature, there are many proposals discussing bimodal distributions; e.g., the works of [7][8][9][10][11][12]. Bimodal data can be fitted by a mixture of two unimodal distributions. ...

... To answer such question, we consider the Lambert-F distribution generator [8] defined by the cumulative distribution function (cdf) given by G(x; α) = 1 − [1 − F(x)]α F(x) , where α ∈ (0, e) is a shape parameter, e ≈ 2.718 is the Euler's number and F(x) is an arbitrary baseline cdf. This generator has the particularity that the inverse function, that is, the quantile function, can be expressed in closed form in terms of the Lambert W function defined in Appendix A. If the baseline distribution F(x) is symmetric, it can be verified that α performs as a skewness parameter, allowing asymmetric shapes for the resulting pdf (for more details, see Iriarte et al. [9]). ...

... The relevance of the statistical analysis of the distributions (3) and (4), and their particular types and mixtures is evidenced by a large number of publications on this topic, for example, the Refs. [10][11][12][13][14][15][16][17][18][19]. ...

... The methods applied in the present paper can be considered as extensions and alternatives to the well-known skew-normal distribution (see [5,12]), whose properties (see [12,13]), and corresponding estimation [14] have been widely discussed. Other ways of obtaining skewed normal distributions have also been introduced, such as the one proposed by Reference [15], the Balakrishnan skew-normal density in Reference [16], the proposed model of Reference [17] and the generalized normal distribution in References [18][19][20], among others. For an exhaustive and comprehensive study of the skew-normal distribution, see the recent book by Reference [21]. ...

... The main aim of the authors was to generate a model with a higher kurtosis that allows better modeling of positive data in the presence of outliers. Other authors have worked on a similar idea, e.g., Iriarte et al. [7], Reyes et al. [8], Olmos et al. [9], Segovia et al. [10], and Astorga et al. [11]. ...

... Specifically, for α = 0 and θ = (2σ) −1 , the MSGR model is reduced to the modified slashed Rayleigh distribution [27]. If α = −1/2 and θ = (2σ 2 ) −1 , then the MSGR reduces to the modified slashed half-normal distribution [28]. For α = 1/2 and θ = σ/2, we get the modified slashed Maxwell distribution. ...

... Note that these data present a high level of kurtosis. Table 3 presents ML estimates and SE (in parentheses) for the transmuted generalized half-normal (TGHN) [16], Lindley-Weibull (LW) [17], exponentiated BS normal (EXPBSn) [18], and SQG distributions. For each model, the maximum value of the log-likelihood functions (LLF), the corresponding values for the Akaike information criterion (AIC) [19], and Bayesian information criterion (BIC) [20] are also shown. ...

Reference: A Gamma-Type Distribution with Applications

... It has a stochastic representation as ZU − 1 the modified slashed Birnbaum-Saunders distribution and concluded that it has greater kurtosis values than the usual BSdistribution. Similar to this methodology, the slashed Lindley-Weibull distribution was introduced by Reyes et al. [17]; the slashed power Lindley distributions was studied by Iriarte et al. [18]; and the modified slashed generalized exponential distribution was introduced by Astorga et al. [19]. ...