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This paper introduces a general family of continuous distributions, based on the exponential-logarithmic distribution and the odd transformation. It is called the "odd exponential logarithmic family". We intend to create novel distributions with desired qualities for practical applications, using the unique properties of the exponential-logarithmic distribution as an initial inspiration. Thus, we present some special members of this family that stand out for the versatile shape properties of their corresponding functions. Then, a comprehensive mathematical treatment of the family is provided, including some asymptotic properties, the determination of the quantile function, a useful sum expression of the probability density function, tractable series expressions for the moments, moment generating function, Rényi entropy and Shannon entropy, as well as results on order statistics and stochastic ordering. We estimate the model parameters quite efficiently by the method of maximum likelihood, with discussions on the observed information matrix and a complete simulation study. As a major interest, the odd exponential logarithmic models reveal how to successfully accommodate various kinds of data. This aspect is demonstrated by using three practical data sets, showing that an odd exponential logarithmic model outperforms two strong competitors in terms of data fitting. [ABSTRACT FROM AUTHOR]

A new family of distributions called the odd generalized N-H is introduced and studied. Four new special models are presented. Some mathematical properties of the odd generalized N-H family are studied. Explicit expressions for the moments, probability weighted, quantile function, mean deviation, order statistics and Rényi entropy are investigated. Characterizations based on the truncated moments, hazard function and conditional expectations are presented for the generated family. Parameter estimates of the family are obtained based on maximum likelihood procedure. Two real data sets are employed to show the usefulness of the new family. [ABSTRACT FROM AUTHOR]

We propose a new generator of continuous distributions, so called the transmuted generalized odd generalized exponential-G family, which extends the generalized odd generalized exponential-G family introduced by Alizadeh et al. (2017). Some statistical properties of the new family such as; raw and incomplete moments, moment generating function, Lorenz and Bonferroni curves, probability weighted moments, Rényi entropy, stress strength model and order statistics are investigated. The parameters of the new family are estimated by using the method of maximum likelihood. Two real applications are presented to demonstrate the effectiveness of the suggested family. [ABSTRACT FROM AUTHOR]

This article introduces a new generalization of the transmuted exponentiated modified Weibull distribution introduced by Eltehiwy and Ashour in 2013, using Kumaraswamy distribution introduced by Cordeiro and de Castro in 2011. We refer to the new distribution as Kumaraswamy-transmuted exponentiated modified Weibull (Kw-TEMW) distribution. The new model contains 54 lifetime distributions as special cases such as the KumaraswamyWeibull, exponentiated modified Weibull, exponentiated Weibull, exponentiated exponential, transmuted Weibull, Rayleigh, linear failure rate, and exponential distributions, among others. The properties of the new model are discussed and the maximum likelihood estimation is used to evaluate the parameters. Explicit expressions are derived for the moments and examine the order statistics. This model is capable of modeling various shapes of aging and failure criteria. [ABSTRACT FROM AUTHOR]

Tiao and Lund [The use of OLUMV estimators in inference robustness studies of the location parameter of a class of symmetric distributions. J Amer Statist Assoc. 1970;65(329):370–386] tabulated the coefficients of the best linear unbiased estimators (BLUEs) of location and scale for a particular family of symmetric distributions. This family was a reparameterization of the extended exponential power distribution (EEPD) with the shape parameter restricted to be greater than or equal to one. In this work, we consider the BLU estimation of the location and scale parameters of the EEPD when the shape parameter is one-third and one-half. We obtain closed-form expressions for the single and product moments of the order statistics when the shape parameter is in general in the form of a reciprocal of an integer. These expressions are then used to determine the BLUEs and the corresponding variances for complete samples of size 20 and less. We consider some other linear estimators of the location and scale parameters and then compare them with the BLUEs. Finally, we present a numerical example to illustrate the developed results. [ABSTRACT FROM PUBLISHER]

A generalized k-out-of-n system which is denoted by ((n1,\ldots,nN),f,k) consists of N modules ordered in a line or a circle, and the ith module is composed of ni components in parallel (ni\geq 1,i=1,\ldots,N). The system fails iff there exist at least f failed components or at least k consecutive failed modules. In this paper, we compute the signature of this system when n1=\ldots=nN=n, and present illustrative examples to demonstrate its application. Simulation based computation of the signature is provided when the modules have different numbers of components. [ABSTRACT FROM AUTHOR]

In this article, the Pitman closeness of upper and lowerk-records to progressive Type-II censored order statistics for location-scale families is investigated. In each case, the special properties of the probability of Pitman closeness are obtained and the corresponding monotonicity properties are discussed. Moreover, the closestk-record to a specific progressive Type-II censored data is obtained. Finally, for the standard exponential and standard uniform distributions, explicit expressions for the probability of Pitman closeness are derived. For various censoring schemes, the results of the numerical computations are displayed in tables. Most of the results in Ahmadi and Balakrishnan (2013) can be achieved as special cases. [ABSTRACT FROM AUTHOR]

The Farlie-Gumbel-Morgenstern (FGM) family of bivariate distributions is widely used in practice. Here, we present some distributional properties of the concomitants of bivariate FGM family. Concomitants are the Y-variates associated with the ordered X-variate from a bivariate distribution F(X,Y). In some applications only available data are the concomitants. Based on these distributional properties, we address the concomitants of generalized order statistics for some popular probability model. In particular, the estimations of location and scale parameters of the bivariate FGM family of distributions when the marginal distributions are exponential, power function and Pareto are obtained. Further, we provide the MVLUE estimators of the location, scale and an unbiased estimator of the dependence parameter of the distribution. [ABSTRACT FROM AUTHOR]

It is well known that a ranked set sample under perfect ranking provides more information than an i.i.d. sample of the same size. Then it may be interesting to study how much information is lost due to imperfect ranking. In this article, we consider some ranking mechanisms and study the loss of the Fisher information according to the degree of imperfect ranking. Then we continue to discuss the optimal combination of the sample size and number of strata in terms of maximizing the Fisher information for the bivariate normal and exponential distributions. [ABSTRACT FROM AUTHOR]

Generalized order statistics, and thus sequential order statistics with conditional proportional hazard rates, are shown to form a regular exponential family in the model parameters. This structure is utilized to derive maximum likelihood estimators for these parameters or functions of them along with several properties of the estimators. The Fisher information matrix is stated, and asymptotic efficiency is shown. [ABSTRACT FROM PUBLISHER]

The hybrid censoring scheme, which is a mixture of Type-I and Type-II censoring schemes, has been extended to the case of progressive censoring schemes by Kundu and Joarder [Analysis of Type-II progressively hybrid censored data, Comput. Stat. Data Anal. 50 (2006), pp. 2509–2528] and Childs et al. [Exact likelihood inference for an exponential parameter under progressive hybrid censoring schemes, in Statistical Models and Methods for Biomedical and Technical Systems, F. Vonta, M. Nikulin, N. Limnios, and C. Huber-Carol, eds., Birkhäuser, Boston, MA, 2007, pp. 323–334]. In this paper, we derive a simple expression for the Fisher information contained in Type-I and Type-II progressively hybrid censored data. An illustrative example is provided applicable to a scaled-exponential distribution to demonstrate our methodologies. [ABSTRACT FROM PUBLISHER]

Abstract: Based on multiply Type-II censored samples of sequential order statistics, Bayesian estimators are derived for the parameters of one- and two-parameter exponential distributions. In the one-parameter set-up, the posterior density is obtained under the assumption that the prior distribution is given by an inverse Gamma distribution, and the Bayes estimator with respect to squared error loss is calculated. Its performance is illustrated by a numerical example and compared with two non-Bayesian estimators, namely the BLUE and the approximate maximum likelihood estimator (AMLE). Moreover, prediction of future failure times is considered. Minimum risk equivariant estimators and predictors are deduced from the given results. Finally, similar results are presented for the two-parameter situation. [Copyright &y& Elsevier]

This article is concerned with the linear exponential distribution (exponential and Rayleigh distributions). Recurrence relations for single and product moments of generalized order statistics have been derived. Single and product moments of ordinary order statistics and upper k-records cases have been discussed as special cases from generalized order statistics. Explicit expressions for single and product moments of ordinary order statistics and upper record values have been obtained. [ABSTRACT FROM AUTHOR]

Abstract: We modify and extend George and Mudholkar''s [1981. A characterization of the logistic distribution by a sample median. Ann. Inst. Statist. Math. 33, 125–129] characterization result about the logistic distribution, which is in terms of the sample median and Laplace distribution. Moreover, we give some new characterization results in terms of the smallest order statistics and the exponential distribution. [Copyright &y& Elsevier]

Best linear unbiased estimation for parameters of a particular location-scale family based on progressively Type-II censored order statistics is considered and optimal censoring schemes are determined. As optimality criteria serve the ϕp-criteria from experimental design which are applied to the covariance matrix of the BLUEs. The results are supplemented by monotonicity properties of the trace and the determinant with respect to the sample size and the initial number of items in the experiment. [ABSTRACT FROM AUTHOR]

In recent years, several attempts have been made to characterize the generalized Pareto distributions (GPD) based on the properties of order statistics and record values. In the present article, we give some characterization results on GPD based on order statistics and generalized order statistics. Some characterizations of uniform distribution based on expectation of some functions of order statistics are also given. [ABSTRACT FROM AUTHOR]

In this paper we consider the problem of unbiased estimation of the distribution function of an exponential population using order statistics based on a random sample. We present a (unique) unbiased estimator based on a single, say i th, order statistic and study some properties of the estimator for i = 2. We also indicate how this estimator can be utilized to obtain unbiased estimators when a few selected order statistics are available as well as when the sample is selected following an alternative sampling procedure known as ranked set sampling. It is further proved that for a ranked set sample of size two, the proposed estimator is uniformly better than the conventional nonparametric unbiased estimator, further, for a general sample size, a modified ranked set sampling procedure provides an unbiased estimator uniformly better than the conventional nonparametric unbiased estimator based on the usual ranked set sampling procedure. [ABSTRACT FROM AUTHOR]

The author proposes the best shrinkage predictor of a preassigned dominance level for a future order statistic of an exponential distribution, assuming a prior estimate of the scale parameter is distributed over an interval according to an arbitrary distribution with known mean. Based on a Type II censored sample from this distribution, we predict the future order statistic in another independent sample from the same distribution. The predictor is constructed by incorporating a preliminary confidence interval for the scale parameter and a class of shrinkage predictors constructed here. It improves considerably classical predictors for all values of the scale parameter within its dominance interval containing the confidence interval of a preassigned level. [ABSTRACT FROM AUTHOR]

Proposes optimal prediction intervals for the exponential distribution based on generalized order statistics (GOS). Estimation and prediction for the first future GOS; Prediction problems of the life time models associated with the exponential distribution.

The analysis of stress-strength systems is connected to the probability P(X < Y), where X represents the stress subject to an object and Y is its strength. We consider estimation of P(X < Y) when the underlying data consists of two samples of order statistics from Weinman multivariate exponential distributions with a common location parameter. Maximum likelihood estimators and uniform minimum variance unbiased estimators of P(X < Y) are presented, when the location parameter is assumed to be known and unknown, respectively. Moreover, some distributional properties, a confidence interval and asymptotic results are established. The results can be applied to various data set-ups based on exponential distributions, e.g., ordinary order statistics, progressive type II censored order statistics, sequential order statistics and record values. [ABSTRACT FROM AUTHOR]

Model diagnostic procedures in failure time models using hazard-based residuals rely on the assumption that the residual vector closely resembles a random sample from a unit exponential distribution when the model holds. This article formally investigates the validity of this critical assumption by deriving and examining the properties of parametrically, semiparametrically, and nonparametrically estimated residuals for complete and right-censored data. The joint distribution of the residual vector is characterized, and the behavior of some tests for exponentiality when applied to the residuals is examined analytically and through Monte Carlo methods. Findings reveal that the critical assumption of approximate unit exponentiality of the residual vector may not be viable and, consequently, the model diagnostic procedures considered, which revolve on checking the approximate unit exponentiality of the residual vector (specifically, hazard plotting and the use of spacings and total-time-on-test statistics on the residual vector) may have serious defects. This is especially evident in situations where the failure time distribution is not exponential or when the residuals are obtained nonparametrically in the no-covariate model or semiparametrically in the Cox proportional hazards model. [ABSTRACT FROM AUTHOR]

The problem of estimating the mean of an exponential distribution is studied, when the data available are a random sample of time-censored rth-order statistics. Examples for such empirical situations are cited. Maximum likelihood estimators (MLE's) and moment-equation estimators (MEE's) are studied. Theoretical derivations are provided for the large sample variances and distributions of these estimators. The efficiency of the MEE compared to the MLE is studied. [ABSTRACT FROM AUTHOR]

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This paper presents the small sample optimum choice of the k(≤ τ[sub 2]) order statistics for the best linear unbiased estimate (BLUE) of the parameters μ and σ or σ alone (μ known) when the sample is Type II censored on the right. For n = 2(1)10, k = 1(1)τ[sub 2] and τ[sub 2] = {[.50n]+1} (1)n, the optimum ranks, the coefficients of the BLUEs have been presented in Table I. [ABSTRACT FROM AUTHOR]