Recurrence Relations For Single Moments Research Articles

On the theory of order statistics of the flexible Lomax distribution

This paper studies the flexible Lomax distribution’s order statistics with graphical and numerical findings. Along with the quantitative measurements, some plots are furnished, including those for the skewness and kurtosis measures. We will dwell on the numerous results that relate to statistics of moments of order. We consider the single and product moment of order statistics from the new distribution. Further, we establish some recurrence relation for single moments of order statistics. We have sought to apply the derived relations to empirically evaluate the moments of smallest (largest) order statistics to establish well-known moments and related measures. For order statistics of a flexible Lomax distribution, exact analytical expressions of entropy, residual entropy, and past latent entropy are determined.

Exact Moments of Order Statistics and Parameter Estimation for Sushila Distribution

In this paper, we have obtained the exact expression and recurrence relations for single moments of order statistics arising from Sushila distribution. We have also obtained L-moments, TL-moments of Sushila distribution and used them to find the L-moment and TL-moment estimators of the parameters of the distribution. The estimators of the parameters are also obtained using the method of moments and maximum likelihood. Further, by using these maximum likelihood estimators (MLEs), we have also obtained the MLEs of the measures of reliability of the considered distribution. Monte Carlo simulation has been carried out to investigate the performance of the estimators.

Generalized Exponential Power Distribution with Application to Complete and Censored Data

The exponential power distribution (EP) is a lifetime model that can exhibit increasing and bathtub hazard rate function. This paper proposed a generalization of EP distribution, named generalized exponential power (GEP) distribution. Some properties of GEP distribution will be investigated. Recurrence relations for single moments of generalized ordered statistics from GEP distribution are established and used for characterizing the GEP distribution. Estimation of the model parameters are derived using maximum likelihood method based on complete sample, type I, type II and random censored samples. A simulation study is performed in order to examine the accuracy of the maximum likelihood estimators of the model parameters. Three applications to real data, two with censored data, are provided in order to show the superiority of the proposed model to other models.

Relations for Moments of Dual Generalized Order Statistics from Exponentiated Rayleigh Distribution and Associated Inference

In this paper we obtain exact expressions and some recurrence relations satisfied by single and product moments of dual generalized order statistics from exponentiated Rayleigh distribution. These relations are deduced for moments of order statistics and lower record values. Further, conditional expectation, recurrence relations for single moments and truncated moment are used to characterize this distribution.

The exponentiated burr xii distribution: moments and estimation based on lower record values

In this paper, we have established several explicit expressions and recurrence relations for single and product moments of k-th lower record values from exponentiated Burr XII distribution. Two characterizing results of exponentiated Burr XII distribution has been obtained by using the recurrence relation for single moments and conditional expectation based on lower record values. The method of maximum likelihood is adopted for estimating the model parameters based on k-th lower record values. We carried out Monte Carlo simulations to compare the performances of the proposed methods and providing one real data case study for illustration of the results obtained.

Relations for Moments of Generalized Record Values from Additive Weibull Distribution and Associated Inference

In this note we give some simple recurrence relations satisfied by single and product moments of k-th upper record values from the additive Weibull distribution. These relations are deduced for moments of upper record values. Further, conditional expectation and recurrence relation for single moments are used to characterize the additive Weibull distribution.

The Kumaraswamy-Burr III Distribution Based on Upper Record Values

SYNOPTIC ABSTRACTThis article addresses the problem of frequent estimation of the parameters of the Kumaraswamy-Burr III distribution using upper record values. The explicit expressions and recurrence relations satisfied by the single and product moments of kth upper record values from Kumaraswamy-Burr III distribution are also derived. The corresponding results for upper record values are obtained as special cases. Further, using a recurrence relation for single moments and conditional expectation of record values, we obtain characterization of this distribution. The method of maximum likelihood is adopted for estimating the model parameters. For different parameter settings and sample sizes, various simulation studies have been performed and their performances are compared. Finally, a real data example is discussed to illustrate its applicability.

The Singh–Maddala distribution: properties and estimation

The Singh–Maddala distribution is very flexible and most widely used for modeling the income, wage, expenditure and wealth distribution of the country. Several mathematical and statistical properties of this distribution (such as quantiles, moments, moment generating function, hazard rate, mean residual lifetime, mean deviation about mean and median, Bonferroni and Lorenz curves and various entropies) are derived. We establish relations for the single and product moments of generalized order statistics from the Singh–Maddala distribution and then we use these results to compute the first four moments and variance of order statistics and record values for sample different sizes for various values of the shape and scale parameters. For this distribution, two characterizing results based on conditional moments of generalized order statistics and recurrence relations for single moments are established. The method of maximum likelihood is adopted for estimating the unknown parameters. For different parameters settings and sample sizes, the various simulation studies are performed and compared to the performance of the Singh–Maddala distribution. An application of the model to a real data set is presented and compared with the fit attained by some other well-known two and three parameters distributions.

Moments and Estimation of the Exponentiated Moment Exponential Distribution

A new extension of moment exponential distribution, called exponentiated moment exponential distribution (EMED), was recently introduced by Hasnain [14]. Based on lower generalized order statistics, we first derive the explicit expressions as well as recurrence relations for single and product moments of lower generalized order statistics and we use these results to compute the means, variances and coefficients of skewness and kurtosis of EMED. Further, using a recurrence relation for single moment, we obtain characterization of EMED. Next we obtain the maximum likelihood estimators of the unknown parameters and the approximate confidence intervals of the EMED. Finally, we consider Bayes estimation under the symmetric and asymmetric loss functions using gamma priors for both shape and scale parameters. We have are also derived the Bayes interval of this distribution. Monte Carlo simulations are performed to compare the performances of the proposed methods.

Order Statistics Properties of the Two Parameter Lomax Distribution

In this paper we study the distribution of order statistics of the two parametric Lomax distribution. We consider the single and product moment of order statistics from Lomax distribution. Also, we establish some recurrence relation for single moments of order statistics. The exact analytical expressions of entropy, residual entropy and past residual entropy for order statistics of Lomax distribution is derived.

Relations for moments of k-th record values from exponential-Weibull lifetime distribution and a characterization

In this note we give some recurrence relations satisfied by single and product moments of k-th upper record values from the exponential-Weibull lifetime distribution. Using a recurrence relation for single moments we obtain a characterization of exponential-Weibull, Weibull, exponential, Rayleigh and two parameter linear failure rate distributions.

Recurrence Relations for Moments of Generalized Order Statistics from Marshall – Olkin extended Kumaraswamy distribution and its Characterization

In this paper, Marshall – Olkin extended Kumaraswamy distribution will be obtained. We give some properties for this distribution. Recurrence relations for single and product moments of generalized order statistics from Marshall – Olkin extended Kumaraswamy distribution have been obtained. Specializations to order statistics and records have been made. Further, using a recurrence relation for single moments we obtain characterization of Marshall – Olkin extended Kumaraswamy distribution.

Explict Expressions for Moments of K−TH Lower Record Values from J-Shaped Distribution and a Characterization

In this paper we established some explicit expressions and recurrence relations for single and product moments of k−th lower record values from J-shaped distribution. Further, using a recurrence relation for single moments we obtain characterization of J-shaped distribution.

Recurrence Relations for Moments of Dual Generalized Order Statistics from Weibull Gamma Distribution and Its Characterizations

In this paper, we establish explicit forms and new recurrence relations satisfied by the single and product moments of dua l generalized order statistics from Weibull gamma distribution (WGD). The results include as particular cases the relations for moments of reversed order statistics and lower records. We present characterizations of WGD based on (i) recurrence relation for single moments, (ii) truncated moments of certain function of the variable and (iii) hazrad function.

Recurrence Relations for Moments of k-th Upper Record Values from Flexible Weibull Distribution and a Characterization

In this paper, we establish some recurrence relations satisfied by single and product moments of <i>k-th</i><i> </i>upper record values from the flexible Weibull distribution. We also give a characterization of flexible Weibull distribution by using the recurrence relations for single moments.

Characterization of the Inverse Exponential-Type Distribution based on Recurrence Relations for Dual Generalized Order Statistics

this paper, new recurrence relations satisfied by the single and product moments using moment generating function of dual generalized order statistics from inverse exponential-type distribution are established. Recurrence relations for single and product moments of reversed order statistics and lower record value are obtained as special cases. Further, using a recurrence relation for single moments we obtain characterization of inverse exponential-type distribution. Keywordsgeneralized order statistics, moment generating function, recurrence relations, single moments, product moments, inverse exponential form and characterization.

Recurrence Relations for the Moments of Generalized Inverse Weibull Distribution Based on Lower Records and a Characterization

Abstract—In this study we derive exact expressions and some recurrence relations for single and product moments of lower record values from generalized inverse Weibull distribution. Two theorems on characterization of the generalized inverse Weibull distribution based on conditional expectation of function and the recurrence relation for single moments of lower records are also presented.

Relations for Generalized Order Statistics from Doubly Truncated Generalized Exponential Distribution and its Characterization

In this paper we give some recurrence relations satisfied by single and product moments of generalized order statistics from doubly truncated generalized exponential distribution. These relations are deduced for moments of record values and order statistics. Further, using a recurrence relation for single moments we obtain a characterization of generalized exponential distribution.

Recurrence relations for moments of lower generalized order statistics from Exponentiated Lomax Distribution and its characterization

In this paper, recurrence relations for single and product moments of generalized order statistics from Exponentiated Lomax Distribution have been obtained. Specializations to order statistics and records have been made. Further, using a recurrence relation for single moments we obtain characterization of Exponentiated Lomax Distribution.

Expectation identities of lower generalized order statistics from generalized exponential distribution and a characterization

In this paper, we study the explicit expressions and some recurrence relations for single and product moments of lower generalized order statistics from generalized exponential distribution. The results include as particular cases the above relations for moments of order statistics and lower records. Further, using a recurrence relation for single moments we obtain a characterization of generalized exponential distribution.