Statistica

Estimation of the Parameters of Power Function Distribution based on Progressively Type-II Right Censoring with Binomial Removal

E.I. Abdul Sathar — 2023-09-07

In this article, we proposed the estimates of unknown parameters of power function distribution in the context of progressive type-II censoring with binomial removals, where the number of units removed at each failure time follows a binomial distribution. The maximum-likelihood estimators (MLEs) for the power function parameters are derived using the expectation–maximization (EM) algorithm. EM-algorithm is also used to obtain the asymptotic variance-covariance matrix. By using the variance-covariance matrix of the MLEs, the asymptotic 950=0 confidence interval for the parameters are constructed. Bayes estimators under different loss functions are obtained using the Lindley approximation method and importance sampling procedure. We also introduced one and two sample prediction estimates and corresponding confidence intervals by using Bayesian techniques. To compare performance of the proposed estimators, we introduced simulation and real-life data studies.

The Discrete Power Half-Normal Distribution

Andrea Pallini — 2023-09-07

The discrete power half-normal distribution is introduced, as the discretization of the power halfnormal distribution, based on the difference of values of the continuous survival function. The discrete distribution has a bathtub shaped failure rate or an increasing failure rate. Some statistical properties are proved. Maximum likelihood estimation is studied. A simulation study shows the good asymptotic behaviour of the maximum likelihood estimates. Applications to reliability and lifetime data are provided.

A Muth-Pareto Distribution: Properties, Estimation, Characterizations and Applications

Musaddiq Sirajo — 2023-09-07

In this paper, a new distribution of the Muth-generated family is introduced by considering the Pareto model as baseline with the goal of having increased flexibility and improved goodness of fit in terms of studying tail characteristics. Maximum likelihood estimated parameters of the distribution were found to be consistent and asymptotically unbiased. From a practical point of view, it is shown that the proposed distribution is more flexible than some common statistical distributions. In particular, the proposed model proved to fit well into unimodal data structures. Some mathematical properties were derived, and characterization investigated by truncated first moment where a product of reverse hazard rate and another function of the truncated point is considered. Other characterizations by order statistics and upper record values based on the characterization by the first truncated moment were also established.

On Induced Generalized Record Ranked Set Sampling and its Role in Bivariate Model Building

P. Yageen Thomas — 2023-09-07

A new variety of Ranked Set Sampling (RSS), namely Induced Generalized Record Ranked Set Sampling (IGRRSS), is introduced. In the proposed methodology, ranking is implemented by considering generalized (k) record values on the auxiliary variable X from each sequence of units. The selected units are further screened for measuring the variable of primary interest Y. Further, we propose estimators based on IGRRSS for the unknown parameters associated with the variable Y when the parent bivariate distribution belongs to the Morgenstern family of distributions. The proposed sampling scheme is utilized to collect primary data on the usable timber volume Y based on the ranking of units by generalized (2) record values on tree height X of acacia trees. Accordingly, Morgenstern type bivariate logistic distribution has been modelled for the distribution of the population random vector (X, Y) and estimated the average usable timber volume of the population.

Estimation of the Scale Parameter of Cauchy Distribution Using Absolved Order Statistics

Poruthiyudian Yageen Thomas — 2023-09-07

A new set of ordered random variables generated from a sample from a scale dependent Cauchy distribution known as Absolved Order Statistics (AOS) of the sample forms the problem of investigation in this paper. The distribution theory of these AOS has been developed. The vector of AOS is found to be the minimal sufficient statistic for the Cauchy distribution which is contrary to the existing perception that the vector of order statistics of the sample is minimal sufficient. The best linear unbiased estimate ˆσ of σ based on AOS is derived and its variance is also explicitly expressed. Though only n−4 intermediate order statistics are usable to determine the BLUE of σ based on order statistics, it is found that n−2 AOS are usable to determine ˆσ. This makes ˆσ more efficient estimate of σ than all of its competitors especially when the sample size is small. Illustration for the above result is made through a real life example. It is found that censoring based on AOS is more realistic and the estimate obtained from it for σ is more efficient than the case of censoring with order statistics. A new ranked set sampling known as Adjusted Ranked Set Sampling which is suitable for Cauchy distribution and results with observations distributed as AOS is developed in this paper. Further its role in producing better estimate for σ is analyzed.