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This study introduces a negative Rayleigh detection model for estimating population abundance in line transect surveys. The model satisfies key detection conditions and provides a detailed analysis of its probability density function, moments, and other essential characteristics. Parameters are estimated using three methods: moment estimator, maximum likelihood estimator, and Bayesian estimator. The model's performance is evaluated through simulations, comparing its estimators to those from established models. An empirical application using perpendicular distance data further assesses the model, with goodness-of-fit statistics demonstrating its advantages over traditional methods. [ABSTRACT FROM AUTHOR]

Background: Gross domestic product (GDP) serves as a crucial economic indicator for measuring a country's economic growth, exhibiting both linear and non-linear trends. This study aims to analyze and propose an efficient and accurate time series approach for modeling and forecasting the GDP annual growth rate (%) of Saudi Arabia, a key financial indicator of the country. Methodology: Stochastic linear and non-linear time series modeling, along with hybrid approaches, are employed and their results are compared. Initially, conventional linear and nonlinear methods such as ARIMA, Exponential smoothing, TBATS, and NNAR are applied. Subsequently, hybrid models combining these individual time series approaches are utilized. Model diagnostics, including mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE), are employed as criteria for model selection to identify the best-performing model. Results: The findings demonstrated that the neural network autoregressive (NNAR) model, as a non-linear approach, outperformed all other models, exhibiting the lowest values of MAE, RMSE and MAPE. The NNAR(5,3) projected the GDP of 1.3% which is close to the projection of IMF benchmark (1.9) for the year 2023. Conclusion: The selected model can be employed by economists and policymakers to formulate appropriate policies and plans. This quantitative study provides policymakers with a basis for monitoring fluctuations in GDP growth from 2022 to 2029 and ensuring the sustained progression of GDP beyond 2029. Additionally, this study serves as a guide for researchers to test these approaches in different economic dynamics. [ABSTRACT FROM AUTHOR]

In numerous wastewater treatment processes, the parameters of biological oxygen demand (BOD), chemical oxygen demand (COD), and total suspended solids (TSS) assume a pivotal role. Typically, conventional statistical methods are employed for the surveillance of these three variables. However, in many real-world scenarios, data collection may occur under uncertain conditions, and not all measurements in the dataset are characterized by precision. This research endeavor aims to oversee these critical variables by constructing Hotelling's T 2 control chart using neutrosophic data. The proposed approach utilizes neutrosophic observations of the three variables to create the neutrosophic Hotelling's T 2 (NHT) control chart. Additionally, a comparative analysis has been conducted using the Sullivan and Woodall (SW) method and the Holmes and Mergen (HM) method to assess the effectiveness of each of these methods in detecting shifts and establishing forthcoming production limits. Notably, the SW method exhibits higher sensitivity in shift detection when compared to the HM method. The SW method has been found better for identifying the early shift than that of HM. The mean vector has been computed along with the covariance matrix estimates using both the SW and HM methods to estimate the future production limits. Finally, a MYT-decomposition approach has been employed to identify the sources of variability for each of the three variables. [ABSTRACT FROM AUTHOR]

In this paper, a quantum scheme for a two-qubit system (2QS) and field initially prepared in the excited negative binomial distribution is presented. The field photon statistics is detected from the evolution of the Mandel parameter, while the evolution of von Neumann entropy detects the nonlocal correlation between the 2QS and radiation field. The concurrence is used to detect the qubit-qubit entanglement during the time evolution. The dynamical properties of single-qubit and two-qubit quantum Fisher information are investigated. We visualize the number of photon excitations on the field in negative binomial states with influence of photon success probability. A connection is provided between the dynamical behaviors of these statistical quantities. We have found that the proposed quantities are strongly influenced by the number of excited photons of the field in negative binomial states and photon success probability. [ABSTRACT FROM AUTHOR]

In this paper, the maximum likelihood and Bayesian estimation methods are considered to estimate the unknown parameters, reliability, and hazard rate functions of the Nadarajah–Haghighi (NH) distribution based on adaptive type‐I progressive hybrid censoring (ATIPHC) scheme. The Bayesian estimation is obtained under the assumption of independent gamma priors. The Bayes estimators cannot be obtained in closed form, therefore Lindley's approximation and Markov chain Monte Carlo (MCMC) method are used to solve this problem. The approximate confidence (ACIs) and credible intervals are also considered. To compare the efficiency of the different proposed estimators, a simulation study is considered and the performance of the different estimators are compared using mean square error (MSE) and interval length criterion. Finally, one real data set is analyzed in order to show how these mentioned estimators can be applied in practice. The simulation and real data analysis showed that the Bayes estimates have the smallest MSEs and the BCIs have the smallest lengths compared to their conventional counterparts. [ABSTRACT FROM AUTHOR]

Sine power Lindley distribution (SPLi), a new distribution with two parameters that extends the Lindley model, is introduced and studied in this paper. The SPLi distribution is more flexible than the power Lindley distribution, and we show that in the application part. The statistical properties of the proposed distribution are calculated, including the quantile function, moments, moment generating function, upper incomplete moment, and lower incomplete moment. Meanwhile, some numerical values of the mean, variance, skewness, and kurtosis of the SPLi distribution are obtained. Besides, the SPLi distribution is evaluated by different measures of entropy such as Rényi entropy, Havrda and Charvat entropy, Arimoto entropy, Arimoto entropy, and Tsallis entropy. Moreover, the maximum likelihood method is exploited to estimate the parameters of the SPLi distribution. The applications of the SPLi distribution to two real data sets illustrate the flexibility of the SPLi distribution, and the superiority of the SPLi distribution over some well-known distributions, including the alpha power transformed Lindley, power Lindley, extended Lindley, Lindley, and inverse Lindley distributions. [ABSTRACT FROM AUTHOR]

This article presents the expected Bayesian (E‐Bayesian) estimation of the scale parameter, reliability and failure rate functions of two‐parameter bathtub‐shaped lifetime distribution under type‐II censoring data with. Squared error loss function and gamma distribution as a conjugate prior distribution for the unknown parameter are used to obtain the E‐Bayesian estimators. Also, three different prior distributions for the hyperparameters for the E‐Bayesian estimators are considered. Some properties of the E‐Bayesian estimators are studied. Using minimum mean square error criteria, a simulation study is conducted to compare the performance of the E‐Bayesian estimators and the corresponding Bayes and maximum likelihood estimators. A real data set is analysed to show the applicability of the different proposed estimators. The numerical results show that the E‐Bayesian estimators perform better than the classical and Bayesian estimators. [ABSTRACT FROM AUTHOR]

In this paper, a modified form of the traditional inverse Lomax distribution is proposed and its characteristics are studied. The new distribution which called modified logarithmic transformed inverse Lomax distribution is generated by adding a new shape parameter based on logarithmic transformed method. It contains two shape and one scale parameters and has different shapes of probability density and hazard rate functions. The new shape parameter increases the flexibility of the statistical properties of the traditional inverse Lomax distribution including mean, variance, skewness and kurtosis. The moments, entropies, order statistics and other properties are discussed. Six methods of estimation are considered to estimate the distribution parameters. To compare the performance of the different estimators, a simulation study is performed. To show the flexibility and applicability of the proposed distribution two real data sets to engineering and medical fields are analyzed. The simulation results and real data analysis showed that the Anderson-Darling estimates have the smallest mean square errors among all other estimates. Also, the analysis of the real data sets showed that the traditional inverse Lomax distribution and some of its generalizations have shortcomings in modeling engineering and medical data. Our proposed distribution overcomes this shortage and provides a good fit which makes it a suitable choice to model such data sets. [ABSTRACT FROM AUTHOR]

Understanding a phenomenon fromobserved data requires contextual and efficient statisticalmodels. Such models are based on probability distributions having sufficiently flexible statistical properties to adapt to a maximum of situations. Modern examples include the distributions of the truncated Fréchet generated family. In this paper, we go even further by introducing a more general family, based on a truncated version of the generalized Fr'echet distribution. This generalization involves a new shape parameter modulating to the extreme some central and dispersion parameters, as well as the skewness and weight of the tails. We also investigate the main functions of the new family, stress-strength parameter, diverse functional series expansions, incomplete moments, various entropy measures, theoretical and practical parameters estimation, bivariate extensions through the use of copulas, and the estimation of themodel parameters. By considering a special member of the family having theWeibull distribution as the parent, we fit two data sets of interest, one about waiting times and the other about precipitation. Solid statistical criteria attest that the proposedmodel is superior over other extendedWeibull models, including the one derived to the former truncated Fr'echet generated family. [ABSTRACT FROM AUTHOR]

Products come from different lines with the same facility are tested under comparative life tests which known with the jointly censoring scheme. In this paper, two sets of products under the same facility have Weibull lifetime distributions are selected to test under Type- I generalized hybrid censoring scheme (GHCS). The observed censoring data are used to build the maximum likelihood (ML) estimators as well as approximate confidence intervals for the model parameters. Also, Bayes estimators with the help of MCMC methods are discussed. The analysis of simulated data set with Monte Carlo simulation study is used to illustrate and compare the theoretical results. Finally, a brief comment is summarized in concluding section. [ABSTRACT FROM AUTHOR]

In this article we present a scheme of the interaction between a single qubit (SQ) and radiation field (RF) follows the even "binomial distribution" (BD). The density matrix of the SQ-RF system is given in terms of the number of photon transition and RF distribution parameters. The photon statistics and topographical properties of the RF are quantified by the evolution of Mandel parameter and tomographic entropy respectively. We explore the relation between the tomographic entropy and Wehrl entropy of the RF of the estimators of model parameters in the even BD. The results show that the SQ-RF correlation is connected by the tomographical and statistical properties of the proposed system. [ABSTRACT FROM AUTHOR]