In reliability studies, the best fitting of lifetime models leads to accurate estimates and predictions, especially when these models have nonmonotone hazard functions. For this purpose, the new Exponential‐X Fréchet (NEXF) distribution that belongs to the new exponential‐X (NEX) family of distributions is proposed to be a superior fitting model for some reliability models with nonmonotone hazard functions and beat the competitive distribution such as the exponential distribution and Frechet distribution with two and three parameters. So, we concentrated our effort to introduce a new novel model. Throughout this research, we have studied the properties of its statistical measures of the NEXF distribution. The process of parameter estimation has been studied under a complete sample and Type‐I censoring scheme. The numerical simulation is detailed to asses the proposed techniques of estimation. Finally, a Type‐I censoring real‐life application on leukaemia patient’s survival with a new treatment has been studied to illustrate the estimation methods, which are well fitted by the NEXF distribution among all its competitors. We used for the fitting test the novel modified Kolmogorov–Smirnov (KS) algorithm for fitting Type‐I censored data.

In an endeavor to encapsulate the dual aspects of volatility progression and periodicity inherent in autocorrelation frameworks demonstrated by various nonlinear time series, a novel conceptualization emerges—the periodic threshold autoregressive stochastic volatility (PTAR-SV) model. This model served as a viable alternative to the conventional periodic threshold generalized autoregressive conditional heteroskedasticity (TGARCH) process. The inherent probabilistic framework of the PTAR-SV model incorporated certain essential features, including strict periodic stationarity, enhancing its analytical robustness. Additionally, this study established the conditions for higher-order moments to exist within the PTAR-SV model. The autocovariance structure pertaining to the powers of the PTAR-SV process has been studied. The process of parameter estimation was scrutinized via the quasi-maximum likelihood technique. This estimation approach involved assessing likelihood using prediction error decomposition and Kalman filtering. Moreover, we extended our analysis to include a Bayesian Markov chain Monte Carlo (MCMC) method based on Griddy-Gibbs sampling, particularly suitable when the distribution of model innovations follows a standard Gaussian. Through a simulation study, we evaluated the performances of both the quasi-maximum likelihood (QML) and Bayesian Griddy Gibbs estimates, providing valuable insights into their respective strengths and weaknesses. Finally, we applied our newly developed methodology to model the spot rates of the euro against the Algerian dinar, demonstrating its applicability and efficacy in real-world financial modeling scenarios.

In this study, we explored an asymmetric multivariate stochastic difference volatility model that extends various probabilistic and statistical properties previously discussed in the literature. We rigorously established that the model exhibits periodic stationarity and periodic ergodicity. Additionally, we delved into the robust consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator (QMLE), providing a comprehensive analysis of its theoretical underpinnings. Finally, we demonstrated the practical applicability of our major findings through a series of pertinent applications. This work not only contributes to the existing body of knowledge on stochastic volatility modeling, but also opens new avenues for further research in this domain.

Outlier detection, or anomaly detection as it is known in the machine learning community, has gained interest in recent years, and it is commonly used when the sample size is smaller than the number of variables. In 2015, an outlier detection procedure was proposed 7 for this high-dimensional setting, replacing the classic minimum covariance determinant estimator with the minimum diagonal product estimator. Computationally speaking, their method has two drawbacks: (a) it is not computationally efficient and does not scale up, and (b) it is not memory efficient and, in some cases, it is not possible to apply due to memory limits. We address the first issue via efficient code written in both R and C++, whereas for the second issue, we utilize the eigen decomposition and its properties. Experiments are conducted using simulated data to showcase the time improvement, while gene expression data are used to further examine some extra practicalities associated with the algorithm. The simulation studies yield a speed-up factor that ranges between 17 and 1800, implying a successful reduction in the estimator’s computational burden.