Properties of reverse hazard functions

Chechile, Richard A.

doi:10.1016/j.jmp.2011.03.001

Cited by 45 publications

(34 citation statements)

References 66 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, several distributions with L = −∞ such as normal, logistic, and Gumbel as well as distributions with finite L such as gamma and Weibull have decreasing reversed hazard rate. For other examples and relations, we refer the reader to Chechile [11]. Now, we focus on unimodality properties of the distribution of lower k-record values.…”

Section: Lemma 22: Suppose That the Reversed Hazard Rate R Is Logconmentioning

confidence: 99%

See 1 more Smart Citation

SOME CONVEXITY PROPERTIES OF THE DISTRIBUTION OF LOWER k-RECORD VALUES WITH EXTENSIONS

Alimohammadi

Alamatsaz

Cramer³

2014

Prob. Eng. Inf. Sci.

View full text Add to dashboard Cite

Unimodality and strong unimodality of the distribution of ascendingly ordered random variables have been extensively studied in the literature, whereas these properties have not received much attention in the case of descendingly ordered random variates. In this paper, we show that log concavity of the reversed hazard rate implies that of the density function. Using this fundamental result, we establish some convexity properties of such random variables. To do this, we first provide a counterexample showing that a claim of Basak & Basak [7] about the lower record values is not valid. Then, we provide conditions under which unimodality properties of the distribution of lower k-record values would hold. Finally, some extensions to dual generalized order statistics in both univariate and multivariate cases are discussed.

show abstract

Section: Lemma 22: Suppose That the Reversed Hazard Rate R Is Logconmentioning

confidence: 99%

“…Comparing (10) with (11), we find that even by adding the condition of monotonicity of f , the quantity inside the brackets on the right-hand side of (10) cannot be non-increasing in x, but this is the case for (11).…”

Section: Remark 25mentioning

confidence: 99%

SOME CONVEXITY PROPERTIES OF THE DISTRIBUTION OF LOWER k-RECORD VALUES WITH EXTENSIONS

Alimohammadi

Alamatsaz

Cramer³

2014

Prob. Eng. Inf. Sci.

View full text Add to dashboard Cite

show abstract

“…Townsend and Wenger (2004b) The function K(t) is analogous to the integrated hazard function, H(t). If we let k(t) be equal to the density divided by the distribution function, k(t) = f(t)/F(t), then it can be thought of as the conditional probability density that processing completed in just the last instant, given that it completes at or before t. In that sense, k(t)-also termed the reverse hazard function (Chechile, 2011)-is analogous to the hazard function, h(t), which we defined earlier as h(t) = f(t)/S(t), or the probability that a process just completed, given that it had not completed before time t. K(t) is then defined as the integral of k(t) from t to infinity in an analogous way to H(t) being defined as the integral of h (t) from 0 to t. Furthermore, in analogy to…”

Section: And Taskmentioning

confidence: 99%

Workload capacity spaces: A unified methodology for response time measures of efficiency as workload is varied

2011

View full text Add to dashboard Cite

Increasing the number of available sources of information may impair or facilitate performance, depending on the capacity of the processing system. Tests performed on response time distributions are proving to be useful tools in determining the workload capacity (as well as other properties) of cognitive systems. In this article, we develop a framework and relevant mathematical formulae that represent different capacity assays (Miller's race model bound, Grice's bound, and Townsend's capacity coefficient) in the same space. The new space allows a direct comparison between the distinct bounds and the capacity coefficient values and helps explicate the relationships among the different measures. An analogous common space is proposed for the AND paradigm, relating the capacity index to the Colonius-Vorberg bounds. We illustrate the effectiveness of the unified spaces by presenting data from two simulated models (standard parallel, coactive) and a prototypical visual detection experiment. A conversion table for the unified spaces is provided.

show abstract

“…In the continuous case, the reversed hazard rate, r(x), is defined as the quotient between density and cumulative functions (see, e.g., Chechile [4]). In our case, therefore, r(x) = 1 in D and moreover the variable has  as upper limit.…”

Section: Proofmentioning

confidence: 99%

Is there an absolutely continuous random variable with equal probability density and cumulative distribution functions in its support? Is it unique? What about in the discrete case?

Veres-Ferrer

Pavia

2014

International Journal of Advanced Statistics and Probability

View full text Add to dashboard Cite

This paper inquires about the existence and uniqueness of a univariate continuous random variable for which both cumulative distribution and density functions are equal and asks about the conditions under which a possible extrapolation of the solution to the discrete case is possible. The issue is presented and solved as a problem and allows to obtain a new family of probability distributions. The different approaches followed to reach the solution could also serve to warn about some properties of density and cumulative functions that usually go unnoticed, helping to deepen the understanding of some of the weapons of the mathematical statistician's arsenal.

show abstract

Properties of reverse hazard functions

Cited by 45 publications

References 66 publications

SOME CONVEXITY PROPERTIES OF THE DISTRIBUTION OF LOWER k-RECORD VALUES WITH EXTENSIONS

SOME CONVEXITY PROPERTIES OF THE DISTRIBUTION OF LOWER k-RECORD VALUES WITH EXTENSIONS

Workload capacity spaces: A unified methodology for response time measures of efficiency as workload is varied

Is there an absolutely continuous random variable with equal probability density and cumulative distribution functions in its support? Is it unique? What about in the discrete case?

Contact Info

Product

Resources

About