A New Extended Cosine—G Distributions for Lifetime Studies

Sine π -power odd-G family of distributions with applications

This paper investigates a novel category of probability distributions and a specific member within this category. We have formulated a new family of trigonometric distributions by utilizing the odds ratio derived from the distribution function of a base distribution. This newly devised distribution family termed the "Sine pie-power odd-G family" of distributions, is constructed through a transformation involving the sine function. The paper presents an overview of the fundamental characteristics inherent to this proposed distribution family. Using the Weibull distribution as a base reference, we have introduced a member belonging to the proposed distribution family. This member demonstrates various hazard functions such as j, reverse-j, increasing, decreasing, or bathtub shapes. The paper examines essential statistical attributes of this newly introduced distribution. The estimation of the distribution's parameters is carried out via the maximum likelihood estimation method. The accuracy of the parameter estimation procedure is validated through Monte Carlo simulations. The outcomes of these simulations reveal a reduction in biases and mean square errors as sample sizes increase, even for small samples. Two sets of real-engineering data are considered to demonstrate the proposed distribution's applicability. The performance of the suggested distribution is evaluated using some model selection criteria and goodness-of-fit test statistics. Empirical evidence from these evaluations substantiates that the proposed model outperforms six existing models.

A New Extension of the Topp-Leone-Family of Models with Applications to Real Data

In this article, we proposed a new extension of the Topp-Leone family of distributions. Some important properties of the model are developed, such as quantile function, stochastic ordering, model series representation, moments, stress-strength reliability parameter, Renyi entropy, order statistics, and moment of residual life. A particular member called new extended Topp-Leone exponential (NETLE) is discussed. Maximum likelihood estimation (MLE), least-square estimation (LSE), and percentile estimation (PE) are used for the model parameter estimation. Simulation studies were conducted using NETLE to assess the MLE, LSE, and PE performance by examining their bias and mean square error (MSE), and the result was satisfactory. Finally, the applications of the NETLE to two real data sets are provided to illustrate the importance of the NETLG families in practice; the data sets consist of daily new deaths due to COVID-19 in California and New Jersey, USA. The new model outperformed many other existing Topp-Leone's and exponential related distributions based on the real data illustrations.

Modeling to Factor Productivity of the United Kingdom Food Chain: Using a New Lifetime-Generated Family of Distributions

This article proposes a new lifetime-generated family of distributions called the sine-exponentiated Weibull-H (SEW-H) family, which is derived from two well-established families of distributions of entirely different nature: the sine-G (S-G) and the exponentiated Weibull-H (EW-H) families. Three new special models of this family include the sine-exponentiated Weibull exponential (SEWEx), the sine-exponentiated Weibull Rayleigh (SEWR) and sine-exponentiated Weibull Burr X (SEWBX) distributions. The useful expansions of the probability density function (pdf) and cumulative distribution function (cdf) are derived. Statistical properties are obtained, including quantiles (QU), moments (MO), incomplete MO (IMO), and order statistics (OS) are computed. Six numerous methods of estimation are produced to estimate the parameters: maximum likelihood (ML), least-square (LS), a maximum product of spacing (MPRSP), weighted LS (WLS), Cramér–von Mises (CRVM), and Anderson–Darling (AD). The performance of the estimation approaches is investigated using Monte Carlo simulations. The total factor productivity (TFP) of the United Kingdom food chain is an indication of the efficiency and competitiveness of the food sector in the United Kingdom. TFP growth suggests that the industry is becoming more efficient. If TFP of the food chain in the United Kingdom grows more rapidly than in other nations, it suggests that the sector is becoming more competitive. TFP, also known as multi-factor productivity in economic theory, estimates the fraction of output that cannot be explained by traditionally measured inputs of labor and capital employed in production. In this paper, we use five real datasets to show the relevance and flexibility of the suggested family. The first dataset represents the United Kingdom food chain from 2000 to 2019, whereas the second dataset represents the food and drink wholesaling in the United Kingdom from 2000 to 2019 as one factor of FTP; the third dataset contains the tensile strength of single carbon fibers (in GPa); the fourth dataset is often called the breaking stress of carbon fiber dataset; the fifth dataset represents the TFP growth of agricultural production for thirty-seven African countries from 2001–2010. The new suggested distribution is very flexible and it outperforms many known distributions.