We introduce a new model called the Weibull-Lomax distribution which extends the Lomax distribution and has increasing and decreasing shapes for the hazard rate function. Various structural properties of the new distribution are derived including explicit expressions for the moments and incomplete moments, Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time, probability weighted moments, generating and quantile function. The Rényi and q entropies are also obtained. We provide the density function of the order statistics and their moments. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of two real life data sets. For these data, the new model outperforms the McDonald-Lomax, Kumaraswamy-Lomax, gamma-Lomax, beta-Lomax, exponentiated Lomax and Lomax models. 2000 AMS Classi cation: 60E05; 62N05.

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The Weibull-Lomax distribution: properties and applications

Several procedures for the statistical estimation of the regioncharacteristic maximum possible earthquake magnitude, mmax , are currently available. This paper aims to introduce and compare the 12 existing procedures. For each of the procedures given, there are notes on its origin, assumptions made in its derivation, condition for validity, weak and strong points, etc. The applicability of each particular procedure is determined by the assumptions of the model and/or the available information on seismicity of the area.

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Statistical tools for maximum possible earthquake magnitude estimation

The odd Lomax generator of distributions: Properties, estimation and applications

(k, l) [1885]. (n− k + 1) [1753, 1623]. 0 [772]. 0 < ρ < ρ0 [2026]. 1 [772, 548]. $109.95 [2218]. $125.00 [2161]. $129.95 [2259]. 1 ≤ p <∞ [562]. 2 [616, 407]. $229.00 [2019]. 24 [1398]. 24 [1476]. 2s−k [2039]. 3 [852, 2125]. $49.95 [2161]. $59.95 [2219]. $89.95 [2217]. (R) [2002, 1962]. 1 [1276]. 2 [1417]. k [798]. A [1577, 2312, 2346]. α [858, 1840, 2242, 1465, 1271, 1945, 2327, 1926]. AR(1) [1650, 790]. AR(p) [1346]. R̄ [652]. β [668, 856, 497]. c [2332]. χ [919]. D [2135, 2268, 836, 948, 1324, 2309, 2346, 2098, 2176]. δ [1959]. e [596]. E(x⊗ xx′) [1805]. E(xx′ ⊗ xx′) [1805]. F [1901, 915, 1361, 407, 681]. G [548]. Γ [722]. H [1664]. I(1) [845]. K [2308, 1551, 1223, 1837, 368, 479, 2177, 1322, 1198, 2224, 2309, 407, 1932]. k − 2 [1781]. L [439, 1974, 1584, 1399, 1322]. L1 [895]. L2 [2195, 2363, 2039]. LP [562]. LM [1343]. LR [1343]. M [1054, 1107, 2094, 2180]. Lp [1552]. N [816, 752, 48, 1753, 1623, 548]. p [1245, 1461, 2378, 1794, 1868, 1604, 1791, 1589, 2074, 2227]. P (X < Y ) [1867, 1492, 1955]. P (Y < X) [2222, 1380]. Φ [1345]. Pr(a < x < b) [263]. q [1651]. R [1238, 1848, 616, 1932]. r − k [2082, 1480]. R/S [1996]. R = Pr(X > Y ) [2007]. r [1446]. ρ∗ [1884]. S [2151, 1105]. S [848, 790, 909]. σ [1141, 684]. SUNn,2 [2046]. t [1054, 1777, 327, 1533, 1722, 982, 856, 1031, 1780, 1559, 1094, 1391, 1342, 1680]. T 2

/pdf/a-complete-bibliography-of-publications-in-statistical-u76lky1hh4.pdf

A Complete Bibliography of Publications in Statistical Papers

We introduce and study a new three-parameter lifetime distribution named as the inverse power Lomax. The proposed distribution is obtained as the inverse form of the power Lomax distribution. Some statistical properties of the inverse power Lomax model are implemented. Based on censored samples, maximum likelihood estimators of the model parameters are obtained. An intensive simulation study is performed for evaluating the behavior of estimators based on their biases and mean square errors. Superiority of the new model over some well-known distributions is illustrated by means of real data sets. The results revealed the fact that; the suggested model can produce better fits than some well-known distributions.

On the Inverse Power Lomax Distribution

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Statistical Inferences for Lomax Distribution Based on Record Values (Bayesian and Classical)

In this paper, the maximum likelihood and the Bayes estimators are derived for sample from the Generalized-Exponential distribution in the presence of k outliers. These estimators are obtained using Newton-Raphson method and Lindley's approximation (L-approximation). The proposed Bayes estimators are obtained under symmetric and asymmetric loss functions. These estimators are compared empirically using Monte Carlo simulation, when all the parameters are unknown.

Bayesian Approach on the Generalized Exponential Distribution in the Presence of Outliers

The maximum likelihood, moment and mixture of the estimators are for samples from the right truncated exponential distribution The estimators are compared empirically when all the parameters are unknown; their bias and mean square error are investigated with the help of numerical technique We have shown that these estimators are asymptotically unbiased At the end, we conclude that mixture estimators are better than the maximum likelihood and moment estimators

Estimation of parameters of a right truncated exponential distribution

This study investigates Bayesian inference on the reliability parameter $$R=P(X>Y)$$
 from the power Lindley (PL) distribution where X and Y are independent power Lindley random variables Gamma distribution is used as the priors of parameters Bayes and empirical Bayes (EB) approaches are provided in details Based on an EB approach, hyperparameters in the prior distributions, are estimated using the method of moments and maximum likelihood estimates (MLEs) Further, noninformative and less informative priors are opted as the Bayes approaches To estimate the reliability parameter, the posterior mode (PM) and posterior mean methods are obtained Markov Chain Monte Carlo (MCMC) method is performed for the implementation of the posterior mean method The accuracy of the estimation methods involving the MLEs in frequency school and the Bayesian estimate methods are investigated through the Monte Carlo simulations An application example on a real data is performed for illustrative purpose Finally, we will bring this research to the end with discussion on the results

Bayesian approach for the reliability parameter of power Lindley distribution

There are many ways to introduce a shape parameter to an exponential distribution. The different methods may results in variety of weighted exponential (WE) distribution. In this article, we try to estimate the parameters of weighted exponential model, obtained by using the idea of Azzalini, which results in a new class of WE distributions. This new WE model has the probability density function (PDF) whose shape is very close to the shape of the PDF of weibull, gamma or generalized exponential distributions. This model can be used as an alternative to any of these distributions. The maximum likelihood and moment of the estimator are derived for samples from the WE distribution. These estimators are compared empirically when all the parameters are unknown, their bias and determinants are investigated with help of numerical technique, and have shown that moment estimator is unbiased.

Parviz Nasiri

Papers

Statistical Inferences for Lomax Distribution Based on Record Values (Bayesian and Classical)

Bayesian Approach on the Generalized Exponential Distribution in the Presence of Outliers

Estimation of parameters of a right truncated exponential distribution

Bayesian approach for the reliability parameter of power Lindley distribution

Estimation Parameters of the Weighted Exponential Distribution