Estimation of a Discriminant Function Based on Small Sample Size from a Mixture of Two Gumbel Distributions

Ahmad, K.E.; Jaheen, Zeinhum F.; Modhesh, A. A.

doi:10.1080/03610911003624867

Cited by 10 publications

(4 citation statements)

References 23 publications

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“…A set of discriminant functions is used to discriminate multidimensional observations coming from different groups in an optimal way. After that, the classification rule is used to assign observations into one of the possible non-overlapping groups considered during the study [1].…”

Section: P D Amentioning

confidence: 99%

Application of Discriminant Analysis to Predict Students’ Performances in Mathematics in Advanced Secondary Schools

Saidi

Rao

2023

Eur. J. Stat.

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This quantitative study aimed to use discriminant analysis procedures, to develop a classification model to be used for prediction, to predict students’ performances in Mathematics in advanced secondary schools in Tanzania. The study was conducted in Iringa Rural District to model students’ performances in Mathematics in advanced secondary schools owned by the government. Secondary data of students’ performances in Mathematics of 126 students when they were form five in the year 2020/2021 were collected from academic students’ progressive reports and three distinct groups each contained 42 students’ performances were formed. The analysis was done by using R programming software and a seed of 66 was used during the data partitioning to create training and test datasets. The maximum posterior probability rule was used as a classification rule to assign students’ performances in Mathematics into three proposed groups which are: High, Medium and Low. The classification accuracy achieved by the classification model to classify students’ performances in the training dataset is 97.33%. During validation, the model achieved the classification accuracy of 96.08% to classify students’ performances in the test dataset. These findings imply that, the classification model is valid and reliable. Hence the model is convenient to be used for prediction, to predict students’ performances in Mathematics in Advanced Certificate of Secondary Education Examinations.

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Section: P D Amentioning

confidence: 99%

Application of Discriminant Analysis to Predict Students’ Performances in Mathematics in Advanced Secondary Schools

Saidi

Rao

2023

Eur. J. Stat.

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“…Additionally, the family of distributions F IBG is identifiable, meaning different parameters should lead to distinct probability distributions, ensuring a unique maximum for the likelihood function. Ahmad et al (2010) [21] showed the identifiability of the finite mixture of Gumbel distributions; in particular, the family of a Gumbel component F G = {G : G = G(., µ, σ) as (2)} is identifiable. Based on this, we have that the IBG family, F IBG = {F IBG : F IBG (., µ, σ, δ) as (4)}, is identifiable.…”

Section: Parameter Estimationmentioning

confidence: 99%

Bridging Extremes: The Invertible Bimodal Gumbel Distribution

Otiniano,

Silva,

Matsushita

et al. 2023

Entropy

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This paper introduces a novel three-parameter invertible bimodal Gumbel distribution, addressing the need for a versatile statistical tool capable of simultaneously modeling maximum and minimum extremes in various fields such as hydrology, meteorology, finance, and insurance. Unlike previous bimodal Gumbel distributions available in the literature, our proposed model features a simple closed-form cumulative distribution function, enhancing its computational attractiveness and applicability. This paper elucidates the behavior and advantages of the invertible bimodal Gumbel distribution through detailed mathematical formulations, graphical illustrations, and exploration of distributional characteristics. We illustrate using financial data to estimate Value at Risk (VaR) from our suggested model, considering maximum and minimum blocks simultaneously.

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“…the equality H = H implies k = k and The property of the identifiability of various classes of the mixtures has been discussed by several authors, including Teicher (1963), Yakowitz (1968), Al-Hussaini and Ahmad (1981), Ahmad and Abd-El-Hakim (1990), Atienza et al (2006), Sultan et al (2007), Ahmad et al (2010) and Otiniano et al (2015), among others.…”

Section: Properties Of the Mixture Of Two Kumaraswamy Distributionsmentioning

confidence: 99%

MMK for heterogeneous data: identifiability, estimation and application

et al. 2019

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Heterogeneous real datasets need complex probabilistic structures for a correct modeling. On the other hand, several generalizations of the Kumaraswamy distribution have been developed in the past few decades in an attempt to obtain better data adjustments that are limited in the interval (0,1). In this paper, we propose a mixture model of Kumaraswamy distributions (MMK) as a probabilistic structure for heterogeneous datasets with support in (0,1) and as an important generalization of the Kumaraswamy distribution. We derive the moments, the moment-generating function and analyze the failure rate function. Also, we prove the identifiability of the class of all finite mixtures of Kumaraswamy distributions. Via the EM-algorithm, we find estimates of maximum likelihood for the parameters of the MMK. Finally, we test the performance of the estimates by Monte Carlo simulation and illustrate an application of the proposed model using a real dataset.

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Estimation of a Discriminant Function Based on Small Sample Size from a Mixture of Two Gumbel Distributions

Cited by 10 publications

References 23 publications

Application of Discriminant Analysis to Predict Students’ Performances in Mathematics in Advanced Secondary Schools

Application of Discriminant Analysis to Predict Students’ Performances in Mathematics in Advanced Secondary Schools

Bridging Extremes: The Invertible Bimodal Gumbel Distribution

MMK for heterogeneous data: identifiability, estimation and application

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