Statistics, Optimization & Information Computing

Bayesian Online Change Point Detection for Baseline Shifts

2021-01-26T12:49:45+08:00

In time series data analysis, detecting change points on a real-time basis (online) is of great interest in many areas, such as finance, environmental monitoring, and medicine. One promising means to achieve this is the Bayesian online change point detection (BOCPD) algorithm, which has been successfully adopted in particular cases in which the time series of interest has a fixed baseline. However, we have found that the algorithm struggles when the baseline irreversibly shifts from its initial state. This is because with the original BOCPD algorithm, the sensitivity with which a change point can be detected is degraded if the data points are fluctuating at locations relatively far from the original baseline. In this paper, we not only extend the original BOCPD algorithm to be applicable to a time series whose baseline is constantly shifting toward unknown values but also visualize why the proposed extension works. To demonstrate the efficacy of the proposed algorithm compared to the original one, we examine these algorithms on two real-world data sets and six synthetic data sets.

A New Generalized Modified Weibull Distribution

2021-01-26T12:49:46+08:00

We introduce a new distribution, so called A new generalized modified Weibull (NGMW) distribution. Various structural properties of the distribution are obtained in terms of Meijer's $G$--function, such as moments, moment generating function, conditional moments, mean deviations, order statistics and maximum likelihood estimators. The distribution exhibits a wide range of shapes with varying skewness and assumes all possible forms of hazard rate function. The NGMW distribution along with other distributions are fitted to two sets of data, arising in hydrology and in reliability. It is shown that the proposed distribution has a superior performance among the compared distributions as evidenced via goodness--of--fit tests

Applications of Some Rating Methods to Solve Multicriteria Decision-Making Problems

2021-01-26T12:49:46+08:00

This study proposes a new approach for the solution of multicriteria decision-making problems. The proposed approach is based on using rating/ranking methods. Particularly, in this paper, we investigate the possibility of applying Massey, Colley, Keener, offence-defence, and authority-hub rating methods, which are successfully used in various fields. The proposed approach is useful when no decision-making authority is available or when the relative importance of various criteria has not been previously evaluated. The proposed approach is tested with an example problem to demonstrate its viability and suitability for application.

Inferences for Weibull parameters under progressively first-failure censored data with binomial random removals

2021-01-26T12:49:46+08:00

In this paper, the Bayesian and non-Bayesian estimation of a two-parameter Weibull lifetime model in presence of progressive first-failure censored data with binomial random removals are considered. Based on the s-normal approximation to the asymptotic distribution of maximum likelihood estimators, two-sided approximate confidence intervals for the unknown parameters are constructed. Using gamma conjugate priors, several Bayes estimates and associated credible intervals are obtained relative to the squared error loss function. Proposed estimators cannot be expressed in closed forms and can be evaluated numerically by some suitable iterative procedure. A Bayesian approach is developed using Markov chain Monte Carlo techniques to generate samples from the posterior distributions and in turn computing the Bayes estimates and associated credible intervals. To analyze the performance of the proposed estimators, a Monte Carlo simulation study is conducted. Finally, a real data set is discussed for illustration purposes.

The Weibull Birnbaum-Saunders Distribution And Its Applications

2021-01-26T12:49:47+08:00

A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.

Comparison of two sampling schemes in estimating the stress-strength reliability under the proportional reversed hazard rate model

2021-02-02T06:19:16+08:00

In this paper, point and interval estimation of stress-strength reliability based on lower record ranked set sampling scheme under the proportional reversed hazard rate model are considered. Maximum likelihood, uniformly minimum variance unbiased, and Bayesian estimators of $\mathcal{R}$ are derived and their performances are compared. Various confidence intervals for the parameter $\mathcal{R}$ are constructed, and compared based on the simulation study. Moreover, the record ranked set sampling scheme is compared with ordinary records in case of interval estimations. Finally, a data set has been analyzed for illustrative purposes.

Estimation and Testing Procedures for the Reliability Characteristics of Chen Distribution Based on Type II Censoring and the Sampling Scheme of Bartholomew

2021-01-26T12:49:47+08:00

In this paper, we consider Chen distribution and derive UMVUEs and MLEs of the parameter λ , hazard rate h(t) and the two measures of reliability, namely R(t) = P(X > t), where X denotes the lifetime of an item and P = P(X > Y ), which represents the reliability of an item or system of random strength X subject to random stress Y , under type II censoring scheme and the sampling scheme of Bartholomew . We also develop interval estimates of the reliability measures. Testing procedures for the hypotheses related to different parametric functions have also been developed. A comparative study of different methods of point estimation and average con ddence length has been done through simulation studies. The analysis of a real data set is presented for illustration purpose.

A New Generalized Cauchy Distribution with an Application to Annual One Day Maximum Rainfall Data

2021-01-26T12:49:48+08:00

In this article, we introduce a new three-parameter transmuted Cauchy distribution using
the quadratic rank transmutation map approach. Some mathematical properties of the pro-
posed model are discussed. A simulation study is conducted using the method of maximum
likelihood estimation to estimate the parameters of the proposed model. We used two real data
sets and compare various statistics to show the fitting and versatility of the model.

Hierarchical Forecasting of the Zimbabwe International Tourist Arrivals

2021-01-26T12:49:48+08:00

The objectives of the paper is to: (1) adopt the hierarchical forecasting methods in modelling and forecasting international tourist arrivals in Zimbabwe; and (2) coming up with Zimbabwe international tourist arrivals Prediction Intervals (PIs) in Quantile Regression Averaging (QRA) to hierarchical tourism forecasts. Zimbabwe’s monthly international tourist arrivals data from January 2002 to December 2018 was used. The dataset used was before the COVID-19 period and were disaggregated according to the purpose of the visit (POV). Three hierarchical forecasting approaches, namely top-down, bottom-up and optimal combination approaches were applied to the data. The results showed the superiority of the bottom-up approach over both the top-down and optimal combination approaches. Forecasts indicate a general increase in aggregate series. The combined methods provide a new insight into modelling tourist arrivals. The approach is useful to the government, tourism stakeholders, and investors among others, for decision-making, resource mobilisation and allocation. The Zimbabwe Tourism Authority (ZTA) could adopt the forecasting techniques to produce informative and precise tourism forecasts. The data set used is before the COVID-19 pandemic and the models indicate what could happen outside the pandemic. During the pandemic the country was under lockdown with no tourist arrivals to report on. The models are useful for planning purposes beyond the COVID-19 pandemic.

Testing the Number of Components in a Birnbaum-Saunders Mixture Model under a Random Censoring Scheme

2021-01-26T12:49:48+08:00

This paper deals with testing the number of components in a Birnbaum-Saunders mixture model under randomly right censored data. We focus on two methods, one based on the modified likelihood ratio test and the other based on the shortcut of bootstrap test. Based on extensive Monte Carlo simulation studies, we evaluate and compare the performance of the proposed tests through their size and power. A power analysis provides guidance for researchers to examine the factors that affect the power of the proposed tests used in detecting the correct number of components in a Birnbaum-Saunders mixture model. Finally an example of aircraft Windshield data is used to illustrate the testing procedure.

System Maintenance Using Several Imperfect Repairs Before a Perfect Repair

2021-01-26T12:49:49+08:00

Allowing several imperfect repairs before a perfect repair can lead to a highly reliable and efficient system by reducing repair time and repair cost. Assuming exponential lifetime and exponential repair time, we determine the optimal probability $p$ of choosing a perfect repair over an imperfect repair after each failure. Based on either the limiting availability or the limiting average repair cost per unit time, we determine the optimal number of imperfect repairs before conducting a perfect repair.

A flexible ranked set sampling schemes: Statistical analysis on scale parameter

2021-01-26T12:49:49+08:00

A flexible ranked set sampling scheme including some various existing sampling methods is proposed. This scheme may be used to minimize the error of ranking and the cost of sampling. Based on the data obtained from this scheme, the maximum likelihood estimation as well as the Fisher information are studied for the scale family of distributions. The existence and uniqueness of the maximum likelihood estimator of the scale parameter of the exponential and normal distributions are investigated. Moreover, the optimal scheme is derived via simulation and numerical computations.

Modelling Crude Oil Returns Using the NRIG Distribution

2021-01-26T12:49:49+08:00

Over the past decade, crude oil prices have risen dramatically, making the oil market very volatile and risky; hence, implementing an efficient risk management tool against market risk is crucial. Value-at-risk (VaR) has become the most common tool in this context to quantify market risk. Financial data typically have certain features such as volatility clustering, asymmetry, and heavy and semi-heavy tails, making it hard, if not impossible, to model them by using a normal distribution. In this paper, we propose the subclasses of the generalised hyperbolic distributions (GHDs), as appropriate models for capturing these characteristics for the crude oil and gasoline returns. We also introduce the new subclass of GHDs, namely normal reciprocal inverse Gaussian distribution (NRIG), in evaluating the VaR for the crude oil and gasoline market. Furthermore, VaR estimation and backtesting procedures using the Kupiec likelihood ratio test are conducted to test the extreme tails of these models. The main findings from the Kupiec likelihood test statistics suggest that the best GHD model should be chosen at various VaR levels. Thus, the final results of this research allow risk managers, financial analysts, and energy market academics to be flexible in choosing a robust risk quantification model for crude oil and gasoline returns at their specific VaR levels of interest. Particularly for NRIG, the results suggest that a better VaR estimation is provided at the long positions.

The Impact of International Trade on Central Bank Efficiency: An Application of DEA and Tobit Regression Analysis

2021-01-26T12:49:50+08:00

The purpose of this study is to introduce a novel methodology to measure the central bank efficiency. The data envelopment analysis (DEA) applies in the combination of three input and two output variables characterizing the economic balance in international trade. Super-efficiency DEA model is applied for ranking & comparing the efficiency of different central banks. In contrast, the Malmquist productivity index (MPI) is used to measure the productivity change over the period of time. Further, the study is extended to quantify the impact of international trade dimension on the efficiency of the central bank by using Tobit regression analysis. Finally, based on our data analysis, we reported that the efficiency changes over the period of time and the total productivity changes significantly due to the technology shift as compared to efficiency change. Additionally, it is also observed that the central bank efficiency is impacted dramatically by the export level of the country as compared to import level, average exchange rate and GDP. It implies that the export level of the country significantly influences the performances of the central bank.

Random Polygons and Optimal Extrapolation Estimates of pi

2021-04-02T06:22:46+08:00

We construct optimal extrapolation estimates of π based on random polygons generated by n independent points uniformly distributed on a unit circle in R2. While the semiperimeters and areas of these random n-gons converge to π almost surely and are asymptotically normal as n → ∞, in this paper we develop various extrapolation processes to further accelerate such convergence. By simultaneously considering the random n-gons and suitably constructed random 2n-gons and then optimizing over functionals of the semiperimeters and areas of these random polygons, we derive several new estimates of π with faster convergence rates. These extrapolation improvements are also shown to be asymptotically normal as n → ∞.