Thailand Statistician

Record Values from the Gumbel and q- Gumbel Distributions with Applications

Rasha Abd El-Wahab Attwa, Esraa Osama Ali Abo Zaid — Sun, 29 Sep 2024 00:00:00 +0700

In the present study we investigate the problem of estimating the inherent parameters of the Gumbel and q-Gumbel distributions using record breaking data. We presented the coefficients of the best linear unbiased estimators (BLUE) for location and scale parameters of the Gumbel and q-Gumbel distributions. Finally, the usefulness of our result is illustrated using a simulation study.

One Sample Empirical Likelihood Ratio Test for Coefficient of Variation

Suhas Bhat, Aruna Kalyanpura Rao, Surekha Bhimashankar Munoli — Sun, 29 Sep 2024 00:00:00 +0700

Coefficient of Variation (CV) is widely used as a measure of variation by researchers in applied disciplines like chemistry, engineering, climatology, finance, agriculture and biological sciences. CV is a better measure for analysing health science data as the units of measurement of the index of different organs are often different. To assess precision in immunoassays and morphological measurements, CV is used. The present study aims to propose an empirical likelihood ratio (ELR) test for testing CV. The asymptotic null distribution of the proposed test statistic is obtained as Chi-square distribution with 1 degree of freedom. Simulation is carried out to check the adequacy of Chi-square approximation for finite samples. The proposed test is compared to Wald, bootstrap tests and ELR test constructed by Wang et al. (ELRT2) using real data sets and also simulated data sets. The study indicates that the proposed empirical likelihood ratio test possesses higher power compared to Wald, bootstrap and ELRT2 tests when the underlying distributions considered are normal, lognormal, gamma and Weibull

The Exponentiated Half-Logistic-Generalized Marshall-Olkin-G Family of Distributions with Properties and Applications

Broaderick Oluyede, Peter Ookame Peter, Nkumbuludzi Ndwapi — Sun, 29 Sep 2024 00:00:00 +0700

In this article, we present a new generalized family of distributions called the Exponentiated Half-Logistic-Generalized Marshall-Olkin-G (EHL-GMO-G) distribution. Some of the useful mathematical and statistical properties for this new family of distributions such as the hazard rate function, quantile function, moments and moment generating functions, Renyi entropy, order statistics and ´stochastic order are derived. The method of maximum likelihood estimation is used for estimating the model parameters. Simulation experiments are conducted to illustrate consistency of the maximum likelihood estimates for model parameters and furthermore we apply one special case of this new family to real life data sets to demonstrate its flexibility in modelling various types of real life data

Compound Poisson Correlated Frailty Model Based on Modified Weibull Baseline Distribution for Bivariate Survival Data

Arvind Pandey, Lal Pawimawha — Sun, 29 Sep 2024 00:00:00 +0700

Frailty models are survival models that are used to investigate the features of unobserved heterogeneity in people as it relating to disease and death. Despite their drawbacks, shared frailty models are frequently utilized. Several correlated frailty models were developed over the previous decade to solve these drawbacks. The performance of a compound Poisson correlated frailty model by considering modified Weibull distribution as the model baseline distribution is investigated in this work. The parameters in the proposed models are estimated by adopting Bayesian estimation procedure under the Markov chain Monte Carlo (MCMC) method. In addition, a comparison of the parameters’ true values with estimated values is done using a simulation study. The data from Kidney infection was then used to test the proposed models. Models are compared to existing models using different information criteria and the Bayes factor. Accordingly, the best model for infected patient’s data that have had their catheters inserted has been proposed.

Partial Bayes Estimation in a Normal Family

Babulal Seal, Proloy Banerjee — Sun, 29 Sep 2024 00:00:00 +0700

Areas of Bayesian analysis became vast throughout several decades. Bayes estimation, empirical
and hierarchical Bayes estimation are important areas among them. In multi-parameter case, notion
of ‘Partial Bayes (PB) Estimation’ is introduced and in N(\theta , \sigma ^2), where parameters being unknown,
‘PB Estimation’ of θ is done by putting the estimator of σ2 obtained by some other methods. When
we do not have enough information regarding the joint parameters of the model of the variable and
when we are estimating one parameter in presence of others, such method may be used instead of
empirical and hierarchical methods when the information about their parameters are not sufficient.
Integrated Risk of the PB estimator and Bayes estimator derived under squared error loss function are
compared along with the classical estimator MLE through simulation technique. From the results, it
is found that PB estimator has almost same risk values as that of the Bayes estimator, whereas the risk
of MLE is higher compared to both of the estimator. For illustrative purpose, a real dataset is used to
apply this PB estimation technique. PB is appropriate name to describe. However, partial Bayes term
has been used in different context of Bayesian hierarchical model and meta analysis.

Discrete Gompertz-Lomax Distribution and Its Applications

Watchareewan Chuncharoenkit, Winai Bodhisuwan, Sirinapa Aryuyuen — Sun, 29 Sep 2024 00:00:00 +0700

A new distribution, called the discrete Gompertz-Lomax distribution, is proposed. It has been developed by combining the properties of two existing distributions, namely discrete Gompertz-G family of distributions and Lomax distribution. Its probability mass function is characterized by a flexible probability function that can exhibit unimodality and reverse J-shape (decreasing). It is interesting that some statistical properties of the discrete Gompertz-Lomax distribution have been discussed, including the quantile function, moments, probability generating function, discrete hazard function and discrete reversed hazard function. The maximum likelihood estimation has been formulated to estimate the unknown parameters of the discrete Gompertz-Lomax distribution. A simulation study and applications of this distribution have been illustrated. The development of the discrete Gompertz-Lomax distribution seems to be a valuable contribution to the field of probability theory and statistics. It has potential applications which data with skewed or decreasing patterns may be encountered.

A New Generalized Exponentiated Weibull Distribution: Properties and Applications

Jawad Hussain Ashraf, Zafar Iqbal, Tapan Kumar Chakrabarty — Sun, 29 Sep 2024 00:00:00 +0700

The Weibull distribution is the most important statistical distribution to study the data especially from reliability theory. We propose a new generalized exponentiated Weibull distribution which is developed by using the exponentiated Weibull distribution and exponentiated generalized Weibull distribution. Various well-known lifetime distributions are particular case of the proposed distribution. The failure rate of the newly constructed distribution is monotone and non-monotone such as bathtub, unimodal, increasing and decreasing. Thus, the proposed model seems more flexible. Some important mathematical properties of the proposed distribution are studied and simple expressions for the generating function, moments, mean deviations, entropy, and order statistics density are provided.
Some important aspects of the distribution are also discussed numerically and graphically. Parameters
are estimated by using popular technique of maximum likelihood. We apply newly developed model
to two real data sets and make comparison with some well-known sub-models. We explore that the
proposed model is more flexible and useful as compared to the particular sub-models for modeling
lifetime, skewed and survival time data.

Analyzing Stock Performance in the Banking Sector: Unveiling Value-at-Risk and Conditional Value-at-Risk Strategies

Sun, 29 Sep 2024 00:00:00 +0700

This study explores stock ranking in the banking sector using Value at Risk (VaR) and Conditional Value at Risk (CVaR). The research focuses on bank stocks and employs the Normal Exponential Weighted Moving Average (EWMA) method for volatility calculation and the Historical Simulation Approach for model generation. Data from the Thai stock market’s banking sector, specifically the SET Finance index, is analyzed from January 1, 2017, to December 31, 2021, with confidence levels set at 95 % and 99 %. Model quality is assessed through the Violation Ratio, Three-zone Approach, and Normalized CVaR testing. The findings facilitate stock ranking and aid investors in risk estimation. Results reveal the ranking of banks based on VaR and CVaR, with Bank A identified as the highest-risk bank and Bank B as the lowest-risk bank. Two models, VaR using the Normal EWMA method at the 99% confidence level and CVaR using the Historical Simulation Approach at the 95%
and 99% confidence levels, pass the model quality testing and provide valuable insights for stock
ranking

Precise Average Run Length of an Exponentially Weighted Moving Average Control Chart for Time Series Model

Suvimol Phanyaem — Sun, 29 Sep 2024 00:00:00 +0700

This study aims to develop a precise formula for calculating the average run length in the context of an exponentially weighted moving average (EWMA) control chart, specifically in the presence of a seasonal autoregressive with exogenous variable (SARX(P,r)_L) model. The research also introduces a novel method for estimating the average run length using numerical integral equations, facilitating a comparison between the outcomes derived from the formula and those obtained through the numerical integral equation method. Additionally, control charts are applied to real-world data across diverse domains. The explicit formula is evaluated based on the absolute percentage difference and CPU time. The results show that the average run length calculated using the proposed method precisely corresponds to the findings from the numerical integral equation method. In addition, it’s important to mention that the explicit formulas demonstrated a significant improvement in computational efficiency, requiring much fewer computations than the NIE approach.

Average Run Length Approximation on a Double Exponentially Weighted Moving Average Control Chart through the Numerical Integral Equation Approach

Pornphimol Doktoei, Yupaporn Areepong, Saowanit Sukparungsee — Sun, 29 Sep 2024 00:00:00 +0700

In this paper, we suggest utilizing the midpoint rule, trapezoidal rule, Simpson’s rule, and Gaussian rule in conjunction with the Numerical Integral Equation (NIE) method to estimate the Average Run Length (ARL). These techniques are applied to the Double Exponentially Weighted Moving Average (DEWMA) control chart in situations where the observations follow continuous distributions, like the Weibull and exponential distributions. Furthermore, we contrast the Exponentially Weighted Moving Average (EWMA) control chart’s performance with that of the DEWMA control chart. Out-of-control Average Run Length (ARL₁) and CPU Times are the performance metrics. All of the methods perform similarly, according to the results. It is clear from the results that the DEWMA control chart performs better than the EWMA control chart. Additionally, a wide range of real-world datasets can be used to illustrate the efficacy of the suggested method by applying the NIE method to approximate the ARL.

Is Marital Status a Risk Factor for Mental Disorders? A Case Study

Dibyajyoti Bora, Dhruba Das — Sun, 29 Sep 2024 00:00:00 +0700

In this article, we have studied whether marital status contributes to the occurrence and early onset of mental disorders. Moreover, the impact of mental disorder on present marital status and the simultaneous association of several socio-demographic factors on an affected marital status caused by the disorder were also studied. Data were collected from patients suffering from mental disorders aged 21 years through 60 years. Marital status and the occurrence of mental disorders are independent for both genders. An early-onset age of the disorder for both genders, especially for males is found, male patients have an early onset of 1.6 years compared to females. For both genders, the association between a strained marital life before the occurrence of the disorder and the age of onset of the disorder has been signiﬁcant. After marriage, male patients suffered from mental disorders earlier than their female counterparts. Consequently, the impact of the disorder on present marital status is very worrying with some negative outcomes. The disorder is significantly affecting all categories of marital status. An affected married life is closely associated with disease severity- those with declining illness status and those of younger ages more often reported an affected married life. Among the separated/divorced, 96.6% admit that they are separated/divorced because of the disorder. Male patients were 3.8 times more likely to undergo separation/divorce than females. Although disease severity is the most significant causal factor for affected marital status, simultaneously, some other socio-demographic factors are also found closely associated with the affected status.

Comparison of ARIMAX and Feedforward Neural Network in Forecasting Cash Outflow Inflow at Bank Indonesia East Java Region

Agus Suharsono, Marieta Monica, Bambang Widjanarko Otok, Muhammad Ahsan — Sun, 29 Sep 2024 00:00:00 +0700

Money management, which includes planning, expenditure (outflow), circulation to withdrawal (inflow) in Indonesia, is the duty and authority of the central bank, namely, Bank Indonesia. The amount of money going out and going in needs to be modeled and forecasted to estimate people's money needs in the next period. The effects of calendar variations often affect cash outflows and inflows. Therefore, the method used is ARIMAX with the effect of calendar variations. On the other hand, cash outflow and inflow data allow nonlinear patterns so that the forecasting method used is FFNN. The purpose of this study is to compare the best model between ARIMAX and FFNN in forecasting cash outflow and inflows in the East Java region. There are three Bank Indonesia Representative Offices that are the focus of the research, namely, in the City of Kediri, the City of Jember, and the City of Malang. Not all places can use the ARIMAX and FFNN methods because they adjust the actual data conditions. If the ARIMAX or FFNN criteria do not meet, the modeling continues with ARIMA/SARIMA/Time Series Regression. The criteria for selecting the best model are based on the MSE and RMSE values in the testing data. FFNN modeling is better than ARIMAX on cash inflow data for the city of Kediri and the city of Jember. As for the cash outflow of Jember, ARIMAX is better than FFNN. The rest, compared to ARIMA/SARIMA/Time Series Regression adjusts the actual data pattern. In general, the FFNN model is better than ARIMAX, provided that the data has a nonlinear pattern.

Enhancing Decomposition and Holt-Winters Weekly Forecasting of PM2.5 Concentrations in Thailand’s Eight Northern Provinces Using the Cuckoo Search Algorithm

Watha Minsan, Pradthana Minsan, Wararit Panichkitkosolkul — Sun, 29 Sep 2024 00:00:00 +0700

This research aims to introduce hybrid models that integrate the Cuckoo Search Algorithm with Holt-Winters (CS-HW) and Decomposition (CS-D) for time series forecasting of weekly PM2.5 concentrations in Thailand’s eight northern provinces. The study consists of two phases: the training dataset phase and the testing dataset phase. During the training dataset phase, the Cuckoo Search (CS) algorithm demonstrates effective parameter optimization capabilities, seamlessly integrating with Holt-Winters and decomposition models. This integration results in lower Root Mean Square Error (RMSE) values compared to classical approaches, including Grid Search for Holt-Winters (Classic-HW) and Classical Decomposition (Classic-D). In the testing dataset phase, key performance metrics such as RMSE, Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE) are utilized. The results indicate that the CS-HW and CS-D models outperform other methods in weekly forecasting of PM2.5 concentrations across several provinces, including Chiang Mai, Chiang Rai, Lamphun, Lampang, Mae Hong Son, and Phayao. Notably, the Box-Jenkins model outperformed other methods in Nan, while in Phrae, the Long Short-Term Memory (LSTM) model demonstrates other forecasting performance.

Combined Quality Control Scheme for Monitoring Autocorrelated Process

Dushyant Tyagi, Vipin Yadav — Sun, 29 Sep 2024 00:00:00 +0700

In statistical process control, the control chart helps to diagnose the presence of variation due to assignable causes so that the process can achieve statistical control. There is no doubt that the process exhibiting autocorrelation degrades the functioning of control chart by producing incessant false signals or responding gradually to out-of-control state. The inefficiency of Shewhart control chart to spot small displacements leads to the application of alternate charting techniques like cumulative sum (CUSUM) and exponentially weighted moving average (EWMA). Both CUSUM and EWMA are helpful in detecting small to moderate displacements in the process. A mixed EWMA-CUSUM (MEC) chart was also proposed to improve the detection ability against the smaller shifts. This paper proposed a combined EWMA-MEC quality control scheme to detect small, moderate and large shifts. We fitted an autoregressive process to the autocorrelated observation and applied the charting technique directly to the residuals. Performance measure average run length (ARL) is used to assess the impact of the proposed scheme. We have evaluated ARL of the proposed scheme and compared it with the ARL of MEC, CUSUM and EWMA control charts. The results indicate that the proposed scheme is more sensitive to detecting small to moderate shifts than the previous schemes. We have also discussed the performance of the proposed scheme for the misdesigned charts, i.e., if the shift is different than the anticipated shift, and found that the proposed scheme performs better for the misdesigned cases than the traditional charts.