Author
Carolina Martínez-Riquelme
Bio: Carolina Martínez-Riquelme is an academic researcher from University of Murcia. The author has contributed to research in topics: Random variable & Hazard ratio. The author has an hindex of 7, co-authored 15 publications receiving 202 citations.
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Book•
06 Oct 2015
TL;DR: An Introduction to Stochastic orders discusses the powerful tool that can be used in comparing probabilistic models in different areas such as reliability, survival analysis, risks, finance, and economics as discussed by the authors.
Abstract: An Introduction to Stochastic Orders discusses this powerful tool that can be used in comparing probabilistic models in different areas such as reliability, survival analysis, risks, finance, and economics. The book provides a general background on this topic for students and researchers who want to use it as a tool for their research. In addition, users will find detailed proofs of the main results and applications to several probabilistic models of interest in several fields, and discussions of fundamental properties of several stochastic orders, in the univariate and multivariate cases, along with applications to probabilistic models. * Introduces stochastic orders and its notation* Discusses different orders of univariate stochastic orders* Explains multivariate stochastic orders and their convex, likelihood ratio, and dispersive orders
118 citations
TL;DR: In this paper, a new notion for the comparison of the hazard rates of two random variables taking into account their mutual dependence is defined and studied, and properties, applications and the comparison for a data set are given.
Abstract: In this paper, we define and study a new notion for the comparison of the hazard rates of two random variables taking into account their mutual dependence. Properties, applications and the comparison for a data set are given.
19 citations
18 citations
TL;DR: Sufficient conditions for the excess wealth order are provided based on properties of the quantile functions which are useful when the dispersive order does not hold and it is shown how these results can provide comparisons of quantities of interest in reliability and insurance.
Abstract: The purpose of this paper is twofold. On the one hand, we provide sufficient conditions for the excess wealth order. These conditions are based on properties of the quantile functions which are useful when the dispersive order does not hold. On the other hand, we study sufficient conditions for the comparison in the increasing convex order of spacings of generalized order statistics. These results will be combined to show how we can provide comparisons of quantities of interest in reliability and insurance.
18 citations
TL;DR: Conditions for the mean residual life order based on the ratio of the survival functions are given and can be easily applied to provide results for parametric models and ordered data.
17 citations
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TL;DR: The author does an admirable job of explaining the differences between Bayesian probability and the frequentist notion of probability, showing that, philosophically, only the Bayesian makes sense.
Abstract: (2003). Comparison Methods for Stochastic Models and Risks. Technometrics: Vol. 45, No. 4, pp. 370-371.
611 citations
TL;DR: This book aims to introduce simulation techniques for practitioners in the financial and risk management industry at an intermediate level by having extensive simulation examples using S–PLUS or Visual Basics.
Abstract: (2007). Stochastic Ageing and Dependence for Reliability. Technometrics: Vol. 49, No. 2, pp. 222-222.
314 citations
01 Jan 2016
TL;DR: In this paper, the authors defined the following types of pairs of variables: 0 ≤ p < ∞ [562]. 2 [616, 407]. $229.95 [2259] and 1 ≤ p = p <∞ [548].
Abstract: (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
45 citations
29 Sep 2014
TL;DR: In this article, the basic distribution theory of generalized order statistics is presented and a representation of one and higher dimensional marginal density functions and of the distribution function of a single generalized order statistic are derived and useful properties of them are shown.
Abstract: Several models of ordered random variables are discussed in Section 1. In the distribution theoretical sense, these structures are included in the model of generalized order statistics which we introduce next. Section 3 contains the basic distribution theory of generalized order statistics. Representations of one- and higher dimensional marginal density functions and of the distribution function of a single generalized order statistic are derived and useful properties of them are shown.
40 citations
TL;DR: In this paper, the multiplicative gamma process takes a relevant step in this direction, but improved studies on its properties are required to ease implementation, which is a key topic in statistics, and this note addresses such aim.
40 citations