The Inverse Epsilon Distribution as an Alternative to Inverse Exponential Distribution with a Survival Times Data Example

This paper is devoted to a new flexible two-parameter lower-truncated distribution, which is based on the inversion of the so-called epsilon distribution. It is called the inverse epsilon distribution. In some senses, it can be viewed as an alternative to the inverse exponential distribution, which has many applications in reliability theory and biology. Diverse properties of the new lower-truncated distribution are derived including relations with existing distributions, hazard and reliability functions, survival and reverse hazard rate functions, stochastic ordering, quantile function with related skewness and kurtosis measures, and moments. A demonstrative survival times data example is used to show the applicability of the new model.

Sine Inverse Lomax Generated Family of Distributions with Applications

This paper introduces a new family of distributions by combining the sine produced family and the inverse Lomax generated family. The new proposed family is very interested and flexible more than some old and current families. It has many new models which have many applications in physics, engineering, and medicine. Some fundamental statistical properties of the sine inverse Lomax generated family of distributions as moments, generating function, and quantile function are calculated. Four special models as sine inverse Lomax-exponential, sine inverse Lomax-Rayleigh, sine inverse Lomax-Frèchet and sine inverse Lomax-Lomax models are proposed. Maximum likelihood estimation of model parameters is proposed in this paper. For the purpose of evaluating the performance of maximum likelihood estimates, a simulation study is conducted. Two real life datasets are analyzed by the sine inverse Lomax-Lomax model, and we show that providing flexibility and more fitting than known nine models derived from other generated families.

The New Novel Discrete Distribution with Application on COVID-19 Mortality Numbers in Kingdom of Saudi Arabia and Latvia

This paper aims to introduce a superior discrete statistical model for the coronavirus disease 2019 (COVID-19) mortality numbers in Saudi Arabia and Latvia. We introduced an optimal and superior statistical model to provide optimal modeling for the death numbers due to the COVID-19 infections. This new statistical model possesses three parameters. This model is formulated by combining both the exponential distribution and extended odd Weibull family to formulate the discrete extended odd Weibull exponential (DEOWE) distribution. We introduced some of statistical properties for the new distribution, such as linear representation and quantile function. The maximum likelihood estimation (MLE) method is applied to estimate the unknown parameters of the DEOWE distribution. Also, we have used three datasets as an application on the COVID-19 mortality data in Saudi Arabia and Latvia. These three real data examples were used for introducing the importance of our distribution for fitting and modeling this kind of discrete data. Also, we provide a graphical plot for the data to ensure our results.

Logit Truncated-Exponential Skew-Logistic Distribution with Properties and Applications

In recent years, bounded distributions have attracted extensive attention. At the same time, various areas involve bounded interval data, such as proportion and ratio. In this paper, we propose a new bounded model, named logistic Truncated exponential skew logistic distribution. Some basic statistical properties of the proposed distribution are studied, including moments, mean residual life function, Renyi entropy, mean deviation, order statistics, exponential family, and quantile function. The maximum likelihood method is used to estimate the unknown parameters of the proposed distribution. More importantly, the applications to three real data sets mainly from the field of engineering science prove that the logistic Truncated exponential skew logistic distribution fits better than other bounded distributions.

A SIMPLE NONPARAMETRIC APPROACH FOR ESTIMATION AND INFERENCE OF CONDITIONAL QUANTILE FUNCTIONS

In this paper, we present a new nonparametric method for estimating a conditional quantile function and develop its weak convergence theory. The proposed estimator is computationally easy to implement and automatically ensures quantile monotonicity by construction. For inference, we propose to use a residual bootstrap method. Our Monte Carlo simulations show that this new estimator compares well with the check-function-based estimator in terms of estimation mean squared error. The bootstrap confidence bands yield adequate coverage probabilities. An empirical example uses a dataset of Canadian high school graduate earnings, illustrating the usefulness of the proposed method in applications.

Reliability Analysis of the New Exponential Inverted Topp–Leone Distribution with Applications

The inverted Topp–Leone distribution is a new, appealing model for reliability analysis. In this paper, a new distribution, named new exponential inverted Topp–Leone (NEITL) is presented, which adds an extra shape parameter to the inverted Topp–Leone distribution. The graphical representations of its density, survival, and hazard rate functions are provided. The following properties are explored: quantile function, mixture representation, entropies, moments, and stress–strength reliability. We plotted the skewness and kurtosis measures of the proposed model based on the quantiles. Three different estimation procedures are suggested to estimate the distribution parameters, reliability, and hazard rate functions, along with their confidence intervals. Additionally, stress–strength reliability estimators for the NEITL model were obtained. To illustrate the findings of the paper, two real datasets on engineering and medical fields have been analyzed.

A generalization to the log-inverse Weibull distribution and its applications in cancer research

In this paper we consider a generalization of a log-transformed version of the inverse Weibull distribution. Several theoretical properties of the distribution are studied in detail including expressions for its probability density function, reliability function, hazard rate function, quantile function, characteristic function, raw moments, percentile measures, entropy measures, median, mode etc. Certain structural properties of the distribution along with expressions for reliability measures as well as the distribution and moments of order statistics are obtained. Also we discuss the maximum likelihood estimation of the parameters of the proposed distribution and illustrate the usefulness of the model through real life examples. In addition, the asymptotic behaviour of the maximum likelihood estimators are examined with the help of simulated data sets.

Education, Occupation, and the Cognitive Performance Distribution of South Korean Older Adults

Earlier research suggests that educational attainment up to early adulthood are crucial for the development of cognitive reserve, while intellectually stimulating activities later in the life course are of limited impact. We sought to explore the effects of educational attainment and occupational factors (occupation type and currently having work) across the distribution of cognitive performance for adults aged 45-65 years in South Korea. We analysed scores from the Korean Mini Mental State Exam (MMSE) provided in the 2006 wave of the Korean Longitudinal Study of Aging. We used quantile regressions to both investigate relationships across the distribution and to reduce bias for measures of the central tendency as the MMSE is known for its ceiling effects. The quantile function at the lowest conditional decile of MMSE scores suggested that education level was the dominant significant factor for adult performance on the MMSE (lowest MMSE decile, primary education: β = 6.11 points, p < 0.001; secondary education β = 9.56 points, p < 0.001). All occupational factors were non-significant. Further factors with a significant association with the MMSE were hearing loss, the log-transformed household income, and age squared. With the conditional median function, occupational factors became significant in the middle of the distribution but remained much less important than education levels. In summary, educational levels were more important to explain variation in cognitive functioning than occupational factors, echoing studies with Western samples. We discuss the findings with regard to the historically gender unequal educational and occupational opportunities in Korea.

New extensions of Rayleigh distribution based on inverted-Weibull and Weibull distributions

The Rayleigh distribution was proposed in the fields of acoustics and optics by lord Rayleigh. It has wide applications in communication theory, such as description of instantaneous peak power of received radio signals, i.e. study of vibrations and waves. It has also been used for modeling of wave propagation, radiation, synthetic aperture radar images, and lifetime data in engineering and clinical studies. This work proposes two new extensions of the Rayleigh distribution, namely the Rayleigh inverted-Weibull (RIW) and the Rayleigh Weibull (RW) distributions. Several fundamental properties are derived in this study, these include reliability and hazard functions, moments, quantile function, random number generation, skewness, and kurtosis. The maximum likelihood estimators for the model parameters of the two proposed models are also derived along with the asymptotic confidence intervals. Two real data sets in communication systems and clinical trials are analyzed to illustrate the concept of the proposed extensions. The results demonstrated that the proposed extensions showed better fitting than other extensions and competing models.

Statistical Inference for a General Family of Modified Exponentiated Distributions

In this paper, a modified exponentiated family of distributions is introduced. The new model was built from a continuous parent cumulative distribution function and depends on a shape parameter. Its most relevant characteristics have been obtained: the probability density function, quantile function, moments, stochastic ordering, Poisson mixture with our proposal as the mixing distribution, order statistics, tail behavior and estimates of parameters. We highlight the particular model based on the classical exponential distribution, which is an alternative to the exponentiated exponential, gamma and Weibull. A simulation study and a real application are presented. It is shown that the proposed family of distributions is of interest to applied areas, such as economics, reliability and finances.