A note on the probability of at least successes in correlated binary trials

Zaigraev, Alexander; Kaniovski, Serguei

doi:10.1016/j.orl.2012.10.002

Cited by 14 publications

(10 citation statements)

References 6 publications

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“…Binary choice (response) models have become widespread in practically every area of human activities. In finance, they make it possible to build a forecast as to whether or not a loan will be repaid, or, which is effectively the same, whether or not a borrower will end up in default (Lopez, 2004); in medicine, whether or not a patient will recover (Bakbergenuly et al, 2016); and in production, whether or not equipment will fail (Zaigraev and Kaniovski, 2013). Thus, the primary value of binary choice models is in categorising observations into one of two classes, or, in other words, for dividing into classes or discriminating between classes.…”

Section: Binary Choice Models and The Problem Of Unbalanced Classesmentioning

confidence: 99%

Low Default Portfolios in Basel II and Basel III as a Special Case of Significantly Unbalanced Classes in Binary Choice Models

Penikas¹

2020

RJMF

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In contemporary world, binary choice models are used in many areas. However, for all such areas, a problem arises when the share of one of the classes in the data sample is small. If this share is significantly small, this class is referred to as low default class. The purpose of this paper is to examine the definitions of such a portfolio and the approaches to building models on its basis. Although various methods exist for obtaining results, this paper shows that distinguishing a low default portfolio class, on the one hand, benefits banks, as does any more detailed segmentation, but, on the other hand, it deteriorates the statistical properties of the models for the probability of default. It is therefore justified that for the internal ratingbased approach in the framework of Basel II and Basel III the regulator should require that banks build their models based on combined data sets discouraging them from setting excessive low default portfolio classes.

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Section: Binary Choice Models and The Problem Of Unbalanced Classesmentioning

confidence: 99%

Low Default Portfolios in Basel II and Basel III as a Special Case of Significantly Unbalanced Classes in Binary Choice Models

Penikas¹

2020

RJMF

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“…With this notation, the number of events exceeding a given design value x d 0 during n time steps is defined as

Z false(boldY false) = \sum_{j = 1}^{n} Y_{j}

, where

boldY = ({}, Y_{1}, Y_{2}, \dots, Y_{n})

. For i / n i d Bernoulli trials, Z is distributed as a

scriptP scriptℬ

distribution (Hong, ; Tejada & den Dekker, ; Wang, ; Zaigraev & Kaniovski, ) whose probability mass function (pmf) and cumulative distribution function (cdf) are, respectively,

f_{scriptP scriptℬ} false(z false) = double-struckP false[Z = z false] = \sum_{boldy : Z false(boldy false) = z} \prod_{j = 1}^{n} p_{j}^{y_{j}} {false(1 - p_{j} false)}^{1 - y_{j}},

F_{scriptP scriptℬ} false(z false) = double-struckP false[Z \leq z false] = 1 - \sum_{boldy : Z false(boldy false) \geq false(z + 1 false)} \prod_{j = 1}^{n} p_{j}^{y_{j}} {false(1 - p_{j} false)}^{1 - y_{j}} .

…”

Section: Preliminary Remarks On the Occurrence Of Pot Events Under Inmentioning

confidence: 99%

“…Under nonstationary conditions, the variables Y j are nonidentically distributed with time-varying occurrence probability given by p j = P[Y j = 1]. With this notation, the number of events exceeding a given design value x d0 during n time steps is defined as (Hong, 2013;Tejada & den Dekker, 2011;Wang, 1993;Zaigraev & Kaniovski, 2013) whose probability mass function (pmf ) and cumulative distribution function (cdf ) are, respectively,…”

Section: Preliminary Remarks On the Occurrence Of Pot Events Under Inmentioning

confidence: 99%

Unsurprising Surprises: The Frequency of Record‐breaking and Overthreshold Hydrological Extremes Under Spatial and Temporal Dependence

Serinaldi

Kilsby

2018

Water Resources Research

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Record‐breaking (RB) events are the highest or lowest values assumed by a given variable, such as temperature and precipitation, since the beginning of the observation period. Research in hydroclimatic fluctuations and their link with this kind of extreme events recently renewed the interest in RB events. However, empirical analyses of RB events usually rely on statistical techniques based on too restrictive hypotheses such as independent and identically distributed (i/id) random variables or nongeneral numerical methods. In this study, we propose some exact distributions along with accurate approximations describing the occurrence probability of RB and peak‐over‐threshold (POT) events under general spatiotemporal dependence, which enable analyses based on more appropriate assumptions. We show that (i) the Poisson binomial distribution is the exact distribution of the number of RB events under i/id, (ii) equivalent binomial distributions are accurate approximations under i/id, (iii) beta‐binomial distributions provide the exact distribution of POT occurrences under spatiotemporal dependence, and (iv) equivalent beta‐binomial distributions provide accurate approximations for the distribution of RB occurrences under spatiotemporal dependence. To perform numerical validations, we also introduce a generator of spatially and temporally correlated binary processes, called BetaBitST. As examples of application, we study RB and POT occurrences for monthly precipitation and temperature over the conterminous United States and reanalyze Mauna Loa daily temperature data. Results show that accounting for spatiotemporal dependence yields strikingly different conclusions, making the observed frequencies of RB and POT events much less surprising than expected and calling into question previous results reported in the literature.

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“…We can define the misdetection probability for link i located in CA j when the number of bad samples becomes less than K. The misdetection probability is the summation of the Binomial random variables as before, but the difference is in terms of the correlation between the samples. The summation of the correlated Binomial variables can be found in [21]. In this paper, the detailed mathematical computation is not presented, and we evaluate the performance of the system by simulation.…”

Section: B Network Modelmentioning

confidence: 99%

“…In this paper, the detailed mathematical computation is not presented, and we evaluate the performance of the system by simulation. Let us define p md,i,j as a local misdetection probability, calculated according to [21]. Consider similar AND rule to combine decisions of different MBSs in CA j ∈ C R + .…”

Section: B Network Modelmentioning

confidence: 99%

Mitigation of rain impact on microwave backhaul networks

Yaghoubi

Chen

Rostami

et al. 2016

2016 IEEE International Conference on Communications Workshops (ICC)

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Abstract-Microwave backhaul networks are a cost-efficient option to support increasing capacity demands of mobile networks. However, inherent vulnerability of wireless backhauling to random fluctuations of the wireless channel complicates the design of reliable backhaul links. Long-lasting channel fluctuations such as rain fading may bring significant network performance degradation, and therefore, need to be carefully treated. This paper proposes a novel rain detection algorithm utilizing both temporal and spatial correlation of link status, aiming at efficiently distinguishing between long-term and shortterm channel fading. With this distinction, a central controller decides whether network-wide strategies, such as rerouting, are required to mitigate the effects of rain. The accuracy of the proposed detection method is evaluated by measuring false alarm and misdetection probabilities. Numerical results show high rain detection accuracy of the proposed algorithm. Consequently, the impact of imperfect rain detection on the network throughput performance and on the overhead imposed to the central controller becomes negligible.

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A note on the probability of at least successes in correlated binary trials

Cited by 14 publications

References 6 publications

Low Default Portfolios in Basel II and Basel III as a Special Case of Significantly Unbalanced Classes in Binary Choice Models

Low Default Portfolios in Basel II and Basel III as a Special Case of Significantly Unbalanced Classes in Binary Choice Models

Unsurprising Surprises: The Frequency of Record‐breaking and Overthreshold Hydrological Extremes Under Spatial and Temporal Dependence

Mitigation of rain impact on microwave backhaul networks

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