Analyzing Customers Credit Scoring Criteria in Banking Industry Using Fuzzy Cognitive Mapping Approach

Subject Areas : Operation Research

Samaneh Shariatmadari ¹ , Mahdi Homayounfar ^{2 *} , Keyhan Azadi ³ , Amir Daneshvar ⁴

1 - PhD Candidate, Department of Industrial Management, Rasht Branch, Islamic Azad University, Rasht, Iran
2 - Department of Industrial Management, Rasht Branch, Islamic Azad University, Rasht, Iran
3 - Assistant Professor, Department of Accounting, Rasht Branch, Islamic Azad University, Rasht, Iran
4 - Assistant Professor, Department of Information Technology Management, Electronic Branch, Islamic Azad University, Tehran, Iran

Received: 2023-12-06 Accepted : 2024-04-28 Published : 2024-02-11

Keywords: Credit Scoring, Banking Industry, Criteria, FCM,

Abstract :

Credit scoring is one of the fundamental concepts in bank industry, used for analyzing and evaluating the customers who request for facilities. Because of its importance to its profitability, especially in the developing countries, this study aims to propose a fuzzy cognitive mapping approach for analyzing the potential criteria in credit scoring of legal clients. This research is applied in terms of purpose and survey in terms of method. This research has been conducted in several steps. In the first step, after reviewing the literature, the important factors for scoring the bank's legal clients were identified and 29 criteria out of them were selected. In the next step, a primal evaluation of these criteria by 16 experts, resulted in the 12 more important criteria (total debt ratio, return on assets, ratio of fixed assets to equity, average customer account, customer capital, the ratio of the deferred amount to current assets, ownership ratio (equity to total assets), amount of received facilities, borrowing capacity, amount of requested facility, type of guarantee and credit risk of the last period) were used in the modeling process. Due to the need for fuzzy logic regarding subjective judgments in cause-effect relationships between criteria, fuzzy cognitive mapping (FCM) method was used to visualize the relationships among these factors. The results show that the amount of requested facilities, customer capital, borrowing capacity and amount of received facilities, ratio of fixed assets to equity, and average customer account are the critical criteria in credit scoring of the legal clients.

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Islamic Azad University Rasht Branch ISSN: 2588-5723        E-ISSN:2008-5427

Optimization Iranian Journal of Optimization Volume 15, Issue 4, 2023, 251-255 Research Paper

 

 

                                        Online version is available on: https://sanad.iau.ir/journal/ijo

 

Bayesian Prediction for Chris-Jerry Model Using Unified Progressive Hybrid Censored Sample

 

Hanieh Panahi1* and Sahar Hosseinikhah choshaly 2

 

1 Department of Mathematics and Statistics, Lahijan Branch, Islamic Azad University, Lahijan, Iran

2 Department of Management, Lahijan Branch, Islamic Azad University, Lahijan, Iran

 

 

 

Revise Date: 25 December 2024 Abstract

Keywords: Bayesian point Prediction HPD predictive Chris-Jerry distribution Unified Progressive Hybrid Censoring

Accept Date: 26 December 2024   From a real analysis standpoint, modeling hinges on the choice of the most suitable analysis method, whether it be a frequentist or Bayesian approach, to obtain an updated model. Modeling lifetime data with heavy tail has been a problem among many management researchers. Also, predicting unobserved data based on available data is one of the most important challenges in various sciences such as management and engineering. Bayesian predictive point in Chris-Jerry distribution is considered, in this paper. Te observed data is censored using a unified progressive hybrid censoring scheme. For evidence of the effectiveness of the given methodology, an application is explored.

 

*Correspondence E‐mail: [e-mail]

 

 

INTRODUCTION

   Prediction problems arise naturally in important fields of statistical research and have been very useful in many areas of application such as management, quality control, life experiments and so on. In experiments where failure information is available only on a part of the data, the sample are said to be censored data. Nowadays, the quality and lifetime of any industrial product have become higher because of modern science and technology. Thus, it has become more challenging to increase product qualities with reliability testing in a short period with low expenditure. In this context, censoring is sensible and important to study the failure data in a reliability experiment. Time (Type-I) and (failure) censoring are the most popular censorship techniques. To reduce the cost and duration associated with experiment, progressively Type-II censoring has been developed, which allows the researcher to eliminate items at periods other than the end time. Also, Gorny & Cramer (2018) introduced unified progressive hybrid censoring scheme, where the experimental time may exceed the predetermined time T and the effective sample sizes m, k are prefixed. Let  and  be the two time points. This experiment will be stopped at. In recent years, this censoring and its generalization have been introduced and studied quite extensively (Nagy & Alrasheedi, 2022; Dutta & Kayyal, 2024; Nik et al., 2021; Asadi et al., 2024; Elshahhat & Ashour, 2016).

The Chris-Jerry distribution is a heavy-tailed distribution for analyzing real data (Onyekwere & Obulezi, 2022). It has been introduced as a mixture of two distributions called the exponential (with parameter) and the gamma (with scale and shape parameters as 3 and, respectively) when the mixing proportion is taken as. The positive random variable X, is said to be the Chris-Jerry random variable with parameter  denoted by, if the cumulative distribution function (cdf) is

 

and the probability density function (pdf) is given as

 

For more details, see Onyekwere and Obulezi (2022), Innocent et al. (2023), Obulezi et al. (2023), and Chinedu et al. (2023). For various parameter values, the probability density function (pdf) plot can be shown below.

 

 

 

 

 

 

 

 

 

 

 

Fig. 1. Pdf plot of Chris-Jerry distribution

 

Let denote a unified progressive hybrid censored sample from a  distribution, with censoring scheme. Then, the joint density function of unified progressive hybrid censored order statistics is given by:

 

The remaining portion of the paper is structured as follows. Bayesian predictors and predictive intervals are proposed in Section 2. Section 3 evaluates the estimators’ performance via simulations. Finally, in Section 4, we conclude the study with a brief discussion.

 

BAYESIAN APPROACH

   The Bayes estimation (BE) of the Chris-Jerry distribution under the unified progressive hybrid will be covered in this section. It is assumed that the random variable  follows gamma prior distribution with hyper-parameters  . The prior of  can be given as:

 

The corresponding posterior density given the observed data  is given by:

 

Thus, under the squared error loss function, the BE of any function on model parameters say  , can be obtained as the posterior mean as:

 

Bayesian Prediction

This section deals with the point and interval prediction for -th order statistic out of  removed units based on the unified progressive hybrid sample  with progressive censoring scheme. The conditional density function of, can be formulated as:

 

 

Here,. Considering the cumulative distribution function and density function of the Chris-Jerry model, the conditional density function of  as follows:

 

So, the Bayesian predictive density of  can be written as:

 

To avoid the complexity of the integration given in (9), the Monte Carlo Markov chain samples , for  have been used. So, the -th ordered statistic from the  censored data is given by:

 

SIMULATION STUDIES

This Section is devoted to the comparative study of the proposed estimates under different unified progressive hybrid censored schemes. The simulation is carried out using R software. We considered different values for n, m, k and  to generate 104 unified progressive hybrid censored schemes from the Chris-Jerry model. For given , different censoring schemes are adopted as:

Ø       CSI : 

Ø       CSII :

Ø       CSIII: 

 

 

Table 1: Bayesian point predictors and HPD predictive for.

	k	Censoring Schemes		Point Prediction	Interval Prediction
(60,30)	10	CS I	1	1.67345	1.234	1.875
(60,30)	10		2	1.74324	1.289	1.952
(60,30)	10	CS II	1	1.34832	1.098	1.599
(60,30)	10		2	1.37869	1.112	1.543
(60,30)	10	CS III	1	1.70546	1.249	1.903
(60,30)	10		2	1.72384	1.265	1.937
(60,30)	15	CS I	1	1.79345	1.293	1.917
(60,30)	15		2	1.83552	1.365	2.013
(60,30)	15	CS II	1	1.39894	1.212	1.587
(60,30)	15		2	1.43760	1.268	1.621
(60,30)	15	CS III	1	1.82543	1.378	2.014
(60,30)	15		2	1.86089	1.500	2.112

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

CONCLUSION

   Modeling heavy-tailed data has been a problem among many researchers. One of the common features among standard heavy-tailed distributions is the parsimonious validity of the models in terms of the number of parameters. The new one-parameter Chris-Jerry distribution furnishes a better fit compared to other heavy tailed models, called Lindley, Exponential and Pareto distributions. The Bayes point and interval prediction for observable unified progressive hybrid censored data from the Chris-Jerry model are derived. The results show that the Bayes point predictors lie between the lower and the upper bounds in each case. The lengths of the prediction intervals are decreasing by increasing the effective sample size (k). It has also been observed that different censoring schemes do not have much effect on the simulation results.

REFERENCES

Asadi, S., Panahi, H., & Parviz, P. (2024). Estimation for inverse Burr distribution under generalized progressive hybrid censored data with an application to wastewater engineering data. REVSTAT-Statistical Journal.

Chinedu, E. Q., Chukwudum, Q. C., Alsadat, N., Obulezi, O. J., Almetwally, E. M., & Tolba, A. H. (2023). New lifetime distribution with applications to single acceptance sampling plan and scenarios of increasing hazard rates. Symmetry, 15, Article ID 1881.

Dutta, S., & Kayyal, S. (2024). Estimation and prediction for Burr type III distribution based on unified progressive hybrid censoring scheme. Journal of Applied Statistics, 1–33.

Elshahhat, A., & Ashour, S. (2016). Bayesian and non-Bayesian estimation for Weibull parameters based on generalized Type-II progressive hybrid censoring scheme. Pakistan Journal of Statistics and Operation Research, 12(2), 213–226.

Gorny, J., & Cramer, E. (2018). Modularization of hybrid censoring schemes and its application to unified progressive hybrid censoring. Metrika, 81(2), 173–210.

Innocent, C. F., Frederick, O. A., Udofia, E. M., Obulezi, I. J., & Igbokwe, C. P. (2023). Estimation of the parameters of the power size biased Chris-Jerry distribution. International Journal of Innovative Science and Research Technology, 5, 423–436.

Nik, A. S., Asgharzadeh, A., & Raqab, M. (2021). Estimation and prediction for a new Pareto-type distribution under progressive Type-II censoring. Mathematics and Computers in Simulation, 190, 508–530.

Nagy, M., & Alrasheedi, A. F. (2022). Classical and Bayesian inference using Type-II unified progressive hybrid censored samples for Pareto model. Applied Bionics and Biomechanics, Article ID 2073067.

Obulezi, O. J., Anabike, I. C., & Harrison, E. O. (2023). Marshall-Olkin Chris-Jerry distribution and its applications. International Journal of Innovative Science and Research Technology, 8, 20–31.

Onyekwere, C. K., & Obulezi, O. J. (2022). Chris-Jerry distribution and its applications. Asian Journal of Probability and Statistics, 20(1), 16–30.

 

 

 

Iranian Journal of Optimization, 15(4), 251-255 December 2023 ,2023  2022  2022

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