On Stochastic Comparisons of Largest Order Statistics in the Scale Model

Kochar, Subhash C.; Torrado, Nuria

doi:10.1080/03610926.2014.985839

Cited by 30 publications

(11 citation statements)

References 32 publications

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“…It should be mentioned here that the conditions assumed in Lemmas 3.3-3.5 are commonly used in some previous work such as Khaledi,Farsinezhad,and Kochar [14] and Kochar and Torrado [15]. We will see the universality and generality of these conditions later in Section 4.…”

Section: Resultsmentioning

confidence: 95%

Stochastic Monotonicity of Conditional Order Statistics in Multiple-Outlier Scale Population

Amini-Seresht¹,

Zhang²

2016

Prob. Eng. Inf. Sci.

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This paper discusses the stochastic monotonicity property of the conditional order statistics from independent multiple-outlier scale variables in terms of the likelihood ratio order. Let X1, …, Xn be a set of non-negative independent random variables with Xi, i=1, …, p, having common distribution function F(λ1x), and Xj, j=p+1, …, n, having common distribution function F(λ2x), where F(·) denotes the baseline distribution. Let Xi:n(p, q) be the ith smallest order statistics from this sample. Denote by $X_{i,n}^{s}(p,q)\doteq [X_{i:n}(p,q)|X_{i-1:n}(p,q)=s]$. Under the assumptions that xf′(x)/f(x) is decreasing in x∈ℛ+, λ1≤λ2 and s1≤s2, it is shown that $X_{i:n}^{s_{1}}(p+k,q-k)$ is larger than $X_{i:n}^{s_{2}}(p,q)$ according to the likelihood ratio order for any 2≤i≤n and k=1, 2, …, q. Some parametric families of distributions are also provided to illustrate the theoretical results.

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Section: Resultsmentioning

confidence: 95%

Stochastic Monotonicity of Conditional Order Statistics in Multiple-Outlier Scale Population

Amini-Seresht¹,

Zhang²

2016

Prob. Eng. Inf. Sci.

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“…Khaledi et al [22] studied conditions under which the series and parallel systems consisting of components with lifetimes from scale family of distributions are ordered in terms of the hazard rate and reversed hazard rate orderings, respectively. Kochar and Torrado [27] revisited the problem and obtained a stronger result than the result presented in [22] for the largest order statistics. They established likelihood ratio ordering of the largest order statistics for general scale model.…”

Section: Introductionmentioning

confidence: 88%

Ordering Results on Extremes of Exponentiated Location-Scale Models

Das¹,

Kayal²,

Choudhuri³

2019

Prob. Eng. Inf. Sci.

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In this paper, we consider exponentiated location-scale model and obtain several ordering results between extreme order statistics in various senses. Under majorization type partial order-based conditions, the comparisons are established according to the usual stochastic order, hazard rate order and reversed hazard rate order. Multiple-outlier models are considered. When the number of components are equal, the results are obtained based on the ageing faster order in terms of the hazard rate and likelihood ratio orders. For unequal number of components, we develop comparisons according to the usual stochastic order, hazard rate order, and likelihood ratio order. Numerical examples are considered to illustrate the results.

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“…It was only considered that the demand function is of multiplicative form. Kochar and Torrado () gave stochastic comparisons of largest order statistics in the scale model. Zhen () proposed a stochastic programming model and a robust optimization model from the stochastic perspective to cope with the uncertainty in the tasks’ execution processes.…”

Section: Related Literaturementioning

confidence: 99%

The effect of yield rate in a general price‐setting newsvendor model with a yield‐dependent secondary market

Pei

Liu

et al. 2017

Int Trans Operational Res

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We considered a general price‐setting newsvendor model in which the firm needs to make joint inventory and pricing decisions for short life‐cycle products before the selling season. The firm's production is subject to random yield and the retailer faces uncertain demand. There exists a secondary market for the firm to acquire or dispose of products. We study the effects of yield randomness on optimal decisions and the expected profit in the cost structure, on the condition that the unit prices of the secondary emergency purchase and sale are random functions of the yield. Using the theory of stochastic comparisons, our key findings are as follows. (a) When the unit price of secondary emergency purchase is nonincreasing with the yield realization, a stochastically larger yield rate leads to a higher expected profit for both supply cases. Moreover, for the multiplicative supply case, a stochastically larger yield rate results in a lower optimal sale price, but this is not true in the additive supply case. Numerical examples show that the effect of the yield rate on the optimal order quantity is uncertain for two supply cases. (b) When the unit price of secondary emergency purchase is nonincreasing convexly with the yield realization, a less variable yield rate leads to a higher expected profit for both supply cases. Numerical examples illustrate that the effects of the yield rate on the optimal sale price and the optimal order quantity are also uncertain. (c) Based on graphical comparisons, we find that the effect of yield randomness has a more significant impact on supply chain performance with a yield‐dependent secondary market price than that with a constant secondary market price.

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On Stochastic Comparisons of Largest Order Statistics in the Scale Model

Cited by 30 publications

References 32 publications

Stochastic Monotonicity of Conditional Order Statistics in Multiple-Outlier Scale Population

Stochastic Monotonicity of Conditional Order Statistics in Multiple-Outlier Scale Population

Ordering Results on Extremes of Exponentiated Location-Scale Models

The effect of yield rate in a general price‐setting newsvendor model with a yield‐dependent secondary market

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