Search results for: exponentiated

Authors: Abd El Hady N. Ebraheim

Abstract:

This paper introduces a new generalization of the two parameter Weibull distribution. To this end, the quadratic rank transmutation map has been used. This new distribution is named exponentiated transmuted Weibull (ETW) distribution. The ETW distribution has the advantage of being capable of modeling various shapes of aging and failure criteria. Furthermore, eleven lifetime distributions such as the Weibull, exponentiated Weibull, Rayleigh and exponential distributions, among others follow as special cases. The properties of the new model are discussed and the maximum likelihood estimation is used to estimate the parameters. Explicit expressions are derived for the quantiles. The moments of the distribution are derived, and the order statistics are examined.

Keywords: exponentiated, inversion method, maximum likelihood estimation, transmutation map

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Authors: Srinivasa Rao Gadde

Abstract:

In this article, we considered a group acceptance sampling plans for exponentiated half logistic distribution when the life-test is truncated at a pre-specified time. It is assumed that the index parameter of the exponentiated half logistic distribution is known. The design parameters such as the number of groups and the acceptance number are obtained by satisfying the producer’s and consumer’s risks at the specified quality levels in terms of medians and 10th percentiles under the assumption that the termination time and the number of items in each group are pre-fixed. Finally, an example is given to illustration the methodology.

Keywords: group acceptance sampling plan, operating characteristic, consumer and producer’s risks, truncated life-test

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Authors: A. D. Abdellatif, A. N. Ahmed, M. E. Abdelaziz

Abstract:

The main purpose of this paper is to design a double acceptance sampling plan under the time truncated life test when the product lifetime follows an exponentiated transmuted Weibull distribution. Here, the motive is to meet both the consumer’s risk and producer’s risk simultaneously at the specified quality levels, while the termination time is specified. A comparison between the results of the double and single acceptance sampling plans is conducted. We demonstrate the applicability of our results to real data sets.

Keywords: double sampling plan, single sampling plan, producer’s risk, consumer’s risk, exponentiated transmuted weibull distribution, time truncated experiment, single, double, Marshal-Olkin

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Authors: Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa

Abstract:

A generalized log-logistic distribution with variable shapes of the hazard rate was introduced and studied, extending the log-logistic distribution by adding an extra parameter to the classical distribution, leading to greater flexibility in analysing and modeling various data types. The proposed distribution has a large number of well-known lifetime special sub-models such as; Weibull, log-logistic, exponential, and Burr XII distributions. Its basic mathematical and statistical properties were derived. The method of maximum likelihood was adopted for estimating the unknown parameters of the proposed distribution, and a Monte Carlo simulation study is carried out to assess the behavior of the estimators. The importance of this distribution is that its tendency to model both monotone (increasing and decreasing) and non-monotone (unimodal and bathtub shape) or reversed “bathtub” shape hazard rate functions which are quite common in survival and reliability data analysis. Furthermore, the flexibility and usefulness of the proposed distribution are illustrated in a real-life data set and compared to its sub-models; Weibull, log-logistic, and BurrXII distributions and other parametric survival distributions with 3-parmaeters; like the exponentiated Weibull distribution, the 3-parameter lognormal distribution, the 3- parameter gamma distribution, the 3-parameter Weibull distribution, and the 3-parameter log-logistic (also known as shifted log-logistic) distribution. The proposed distribution provided a better fit than all of the competitive distributions based on the goodness-of-fit tests, the log-likelihood, and information criterion values. Finally, Bayesian analysis and performance of Gibbs sampling for the data set are also carried out.

Keywords: hazard rate function, log-logistic distribution, maximum likelihood estimation, generalized log-logistic distribution, survival data, Monte Carlo simulation

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Authors: Diogo José Morgado Rebelo, Francisco António Carneiro Pacheco de Andrade, Paulo Jorge Freitas de Oliveira Novais

Abstract:

Not everything in AI-power consumer credit scoring turns out to be a wonder. When using AI in Creditworthiness Assessment (CWA), opacity and unfairness ‘sins’ must be considered to the task be deemed Responsible. AI software is not always 100% accurate, which can lead to misclassification. Discrimination of some groups can be exponentiated. A hetero personalized identity can be imposed on the individual(s) affected. Also, autonomous CWA sometimes lacks transparency when using black box models. However, for this intended purpose, human analysts ‘on-the-loop’ might not be the best remedy consumers are looking for in credit. This study seeks to explore the legality of implementing a Multi-Agent System (MAS) framework in consumer CWA to ensure compliance with the regulation outlined in Article 14(4) of the Proposal for an Artificial Intelligence Act (AIA), dated 21 April 2021 (as per the last corrigendum by the European Parliament on 19 April 2024), Especially with the adoption of Art. 18(8)(9) of the EU Directive 2023/2225, of 18 October, which will go into effect on 20 November 2026, there should be more emphasis on the need for hybrid oversight in AI-driven scoring to ensure fairness and transparency. In fact, the range of EU regulations on AI-based consumer credit will soon impact the AI lending industry locally and globally, as shown by the broad territorial scope of AIA’s Art. 2. Consequently, engineering the law of consumer’s CWA is imperative. Generally, the proposed MAS framework consists of several layers arranged in a specific sequence, as follows: firstly, the Data Layer gathers legitimate predictor sets from traditional sources; then, the Decision Support System Layer, whose Neural Network model is trained using k-fold Cross Validation, provides recommendations based on the feeder data; the eXplainability (XAI) multi-structure comprises Three-Step-Agents; and, lastly, the Oversight Layer has a 'Bottom Stop' for analysts to intervene in a timely manner. From the analysis, one can assure a vital component of this software is the XAY layer. It appears as a transparent curtain covering the AI’s decision-making process, enabling comprehension, reflection, and further feasible oversight. Local Interpretable Model-agnostic Explanations (LIME) might act as a pillar by offering counterfactual insights. SHapley Additive exPlanation (SHAP), another agent in the XAI layer, could address potential discrimination issues, identifying the contribution of each feature to the prediction. Alternatively, for thin or no file consumers, the Suggestion Agent can promote financial inclusion. It uses lawful alternative sources such as the share of wallet, among others, to search for more advantageous solutions to incomplete evaluation appraisals based on genetic programming. Overall, this research aspires to bring the concept of Machine-Centered Anthropocentrism to the table of EU policymaking. It acknowledges that, when put into service, credit analysts no longer exert full control over the data-driven entities programmers have given ‘birth’ to. With similar explanatory agents under supervision, AI itself can become self-accountable, prioritizing human concerns and values. AI decisions should not be vilified inherently. The issue lies in how they are integrated into decision-making and whether they align with non-discrimination principles and transparency rules.

Keywords: creditworthiness assessment, hybrid oversight, machine-centered anthropocentrism, EU policymaking

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