Prediction intervals for future Weibull residual data

. Bootstrap methods are widely used statistical techniques known for their simplicity and good properties. This paper introduces a novel bootstrap method called the parametric predictive bootstrap (PP-B), which relies on parametric models and is designed for predictive inference. The PP-B method is evaluated in various scenarios and typically used with other bootstrap methods to assess its performance in estimation and prediction inference. Comparisons of PP-B with other bootstrap methods are made in terms of the coverage probabilities of confidence and prediction intervals. Simulation results indicate that PP-B excels in predictive inference due to its explicitly predictive nature.

Estimation of renewal function under progressively censored data and its applications

Distinguished Author Series articles are general, descriptive representations that summarize the state of the art in an area of technology by describing recent developments for readers who are not specialists in the topics discussed. Written by individuals recognized as experts in the area, these articles provide key references to more definitive work and present specific details only to illustrate the technology. Purpose: to inform the general readership of recent advances in various areas of petroleum engineering. Introduction Monte Carlo simulation is a statistics-based analysis tool that yields probability-vs.-value relationships for key parameters, including oil and gas reserves, capital exposure, and various economic yardsticks, such as net present value (NPV) and return on investment (ROI). These probability relationships help the user answer such questions as "What is the probability that the NPV of this prospect will exceed the target of $1,500,000?" or "How likely is it that the reserves added from this year's exploration program will fall short of our planned production? "Monte Carlo simulation is a part of risk analysis and is sometimes performed in conjunction with or as an alternative to decision [tree] analysis. Putting aside for the moment a description of Monte Carlo simulation, the method has attracted its share of critics over the years. Their comments include "I did this in FORTRAN in 1964, It just never caught on. "; "Why not just add or subtract 10% to the base case?" ; "The answer is whatever you want it to be. "; "The answer depends on who is doing the simulation. "; "Garbage in, garbage out. "; "You never have enough data" ; "A black box, hocus-pocus, that's all it is, "; and "It takes too long to run enough cases. "To some degree, the critics have been silenced by the evolution of virtually universal spreadsheet programs, much faster computers, and relatively simple software to run simulation and process data. Nonetheless, we will address some of the underlying concerns, but it is necessary to lay some foundation first. Our objectives are (1) to define Monte Carlo simulation in a more general context of risk and decision analysis; (2) to provide some specific applications, which can be interrelated; (3) to respond to some of the criticisms; (4) to offer some cautions about abuses of the method and recommend how to avoid the pitfalls; and (5) to predict what the future has in store. What Is Risk Analysis? Although the word "risk" occurs with great regularity these days in the petroleum literature, it has not always been fashionable. In its 60-pageSubject Index, the 1989 printing of the 1,727-page Petroleum Engineering Handbook contains just one reference to "risk [factor]" in an article about property evaluation. Among the numerous words and phrases associated with risk analysis are decision analysis, risk assessment, risk management, portfolio management and optimization, and strategic planning. In some contexts, these words are used only in a qualitative sense, but our focus is quantitative. Decision analysis, in its broadest form, includes problem identification, specification of objectives and constraints, modeling, uncertainty analysis, sensitivity analysis, and rules that lead to a decision. Generally speaking, risk analysis and assessment refer to the quantification of uncertainty, almost always in the context of possible investments. In the oil and gas business, although much of the analysis might pertain to reserve size, capital cost, production forecasting, and the like, the bottom line universally is monetary value. Risk management connotes a second stage, where the investors seek protection from unfavorable situations; i.e., they work to mitigate the risks. Thus, turnkey contracts, guarantees, insurance, locked-in prices, and hedges are instruments of risk management. A portfolio is an aggregation of investments. Portfolio managers mix their prospects to reduce collective risk and enhance ROI. Optimization is often taken as maximizing some measure of reward, such as NPV or profit-to-investment ratio, subject to constraints on risk. Strategic planning involves portfolio management but may include more intangible aspects of investments, such as the advantage of having a presence in a country.

This paper is dedicated to all the researchers for their contributions in reliability theories in the past 50 years. The paper provides a summary on the pioneers of reliability theories, and how their works placed a great influence on our reliability analysis today. This is also a survey paper on reliability theories and methods. The information provided in this paper is mostly based on literatures found first hand to provide as much a neutral view as possible. However, some of the information is adopted from Refs. 1-4. Area of interest in the reliability analysis included representation of reliability parameters, renewal theory, coherent structure, diagram-based models, theoretical methods, and other miscellaneous techniques. Diagram based models included block diagrams, Fault Tree Analysis (FTA), Event Tree Analysis, and flowgraphs. Theoretical methods included queueing theory, asymptotic analysis, Boolean algebra, Bayesian method, Monte Carlo simulation, optimization techniques. Miscellaneous methods that cannot be classified in any of the categories are also provided. Looking back in the last century, a lot of the contributions to reliability research were done in the last 50 years. Weibull, Epstein and Sobel had made a significant influence on the distribution functions we used today. Lotka, Campbell, Feller, Cox, Smith, Barlow, Proschan, Hunter, Marshall, Esary, Gnedenko, Belyaev, and Solov'yev had advanced the theories for reliability. Takacs' paper in sojourn time provided an initiative to the asymptotic studies. Birnbaum started a whole family on component importance measure for coherent structure.

Financialization has contributed to economic growth but has caused scandals, misselling, rogue trading, tax evasion, and market speculation. To a certain extent, it has also created problems in social and economic instability. It is an important aspect of Enterprise Security, Privacy, and Risk (ESPR), particularly in risk research and analysis. In order to minimize the damaging impacts caused by the lack of regulatory compliance, governance, ethical responsibilities, and trust, we propose a Business Integrity Modeling and Analysis (BIMA) framework to unify business integrity with performance using big data predictive analytics and business intelligence. Comprehensive services include modeling risk and asset prices, and consequently, aligning them with business strategies, making our services, according to market trend analysis, both transparent and fair. The BIMA framework uses Monte Carlo simulation, the Black–Scholes–Merton model, and the Heston model for performing financial, operational, and liquidity risk analysis and present outputs in the form of analytics and visualization. Our results and analysis demonstrate supplier bankruptcy modeling, risk pricing, high-frequency pricing simulations, London Interbank Offered Rate (LIBOR) rate simulation, and speculation detection results to provide a variety of critical risk analysis. Our approaches to tackle problems caused by financial services and the operational risk clearly demonstrate that the BIMA framework, as the outputs of our data analytics research, can effectively combine integrity and risk analysis together with overall business performance and can contribute to operational risk research.

Background and Objectives: Cannabidiol (CBD) is increasingly being studied as a therapeutic option for a range of health conditions; however, the pharmacokinetics of CBD is not well understood. This study characterized CBD pharmacokinetics in healthy adults using a population pharmacokinetic approach, informing drug development of oral-based dose forms of CBD. Materials and Methods: CBD concentration-time data were obtained from a phase I, randomized, open-label, four-way crossover study (n=12) and modeled using Phoenix NLME. Monte Carlo simulations were conducted to estimate CBD exposure with chronic dosing as intended for clinical use (50 mg b.i.d.). Results: A three-compartment pharmacokinetic model with a chain of absorption transit compartments and first-order elimination most adequately described CBD pharmacokinetics. Substantial variability in population pharmacokinetic parameters was identified (up to 60%CV), which could not be accounted for by any covariates. Simulations indicated a 3.6-fold difference in drug exposure at steady state with multiple dosing (AUCτ 95% prediction interval: 65.5-138 ng·h/mL), and variability in the time to reach steady state, which was predicted to be up to ∼3 weeks in some individuals (95% prediction interval: 18.6-297 h). Conclusions: The findings of this study have important implications for drug development. The lack of a clear dose-response relationship, due to large pharmacokinetic variability, indicates that a one-size-fits-all approach to CBD dosing may not be feasible, at least with current dosing approaches. Furthermore, an extended time to reach steady state means that the full effect of a selected dose level is not truly observed for some time and requires careful consideration in trial design.

6 Dependence notions in reliability theory

A qualitative risk assessment model for water reuse: Risks related to agricultural irrigation in Brazil

Recent and classical goodness-of-fit tests for the Poisson distribution

Non-Homogeneous Gamma Process (NHGP) is characterized by an arbitrary trend function and a gamma renewal distribution. In this paper, we estimate the confidence intervals of model parameters of NHGP via two parametric bootstrap methods: simulation-based approach and re-sampling-based approach. For each bootstrap method, we apply three methods to construct the confidence intervals. Through simulation experiments, we investigate each parametric bootstrapping and each construction method of confidence intervals in terms of the estimation accuracy. Finally, we find the best combination to estimate the model parameters in trend function and gamma renewal distribution in NHGP.

Inverse sampling is widely applied in studies with dichotomous outcomes, especially when the subjects arrive sequentially or the response of interest is difficult to obtain. In this paper, we investigate the rate ratio test problem under inverse sampling based on gradient statistic with the asymptotic method and parametric bootstrap technique. The gradient statistic has many advantages, for example, it is simple to calculate and competitive with Wald-type, score and likelihood ratio tests in terms of local power. Numerical studies are carried out to evaluate the performance of our gradient test and the existing tests, namely Wald-type, score and likelihood ratio tests. The simulation results suggest that the gradient test based on the parametric bootstrap method has excellent type I error control and large powers even in small sample design. Two real examples, from a heart disease study and a drug comparison study, are applied to illustrate our methods.

Bayesian prediction bounds from the scaled Burr type X model

Classical and Bayesian inferential approaches using Lomax model under progressively type-I hybrid censoring

The intermittence and fluctuation of renewable energy bring significant uncertainty to the power system, which enormously increases the operational risks of the power system. The development of efficient interval prediction models can provide data support for decision making and help improve the economy and reliability of energy interconnection operation. The performance of Bayesian deep learning models and Bayesian shallow neural networks in short-term interval prediction of photovoltaic power is compared in this study. Specifically, an LSTM Approximate Bayesian Neural Network model (ABNN-I) is built on the basis of the deep learning and Monte Carlo Dropout method. Meanwhile, a Feedforward Bayesian Neural Network (ABNN-II) model is introduced by Feedforward Neural Network and the Markov Chain Monte Carlo method. To better compare and verify the interval prediction capability of the ABNN models, a novel clustering method with three-dimensional features which include the number of peaks and valleys, the average power value, and the non-stationary measurement coefficient is proposed for generating sunny and non-sunny clustering sets, respectively. Results show that the ABNN-I model has an excellent performance in the field of photovoltaic short-term interval forecasting. At a 95% confidence level, the interval coverage from ABNN-I to ABNN-II can be increased by up to 3.1% and the average width of the interval can be reduced by 56%. Therefore, with the help of the high computational capacity of deep learning and the inherent ability to quantify uncertainty of the interval forecast from Bayesian methods, this research provides high-quality interval prediction results for photovoltaic power prediction and solves the problem of difficult modeling for over-fitting that exists in the training process, especially on the non-sunny clustering sets.

Uncertainties in spatially aggregated predictions from a logistic regression model