A New Three-Parameter Inverse Weibull Distribution with Medical and Engineering Applications

The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility.This addition is beneficial in a variety of fields,including reliability,economics,engineering,biomedical science,biological research,environmental studies,and finance.For modeling real data,several expanded classes of distributions have been established.The modified alpha power transformed approach is used to implement the new model.The datamatches the new inverseWeibull distribution better than the inverse Weibull distribution and several other competing models.It appears to be a distribution designed to support decreasing or unimodal shaped distributions based on its parameters.Precise expressions for quantiles,moments,incomplete moments,moment generating function,characteristic generating function,and entropy expression are among the determined attributes of the new distribution.The point and interval estimates are studied using the maximum likelihood method.Simulation research is conducted to illustrate the correctness of the theoretical results.Three applications to medical and engineering data are utilized to illustrate the model’s flexibility.

Entropy Bayesian Analysis for the Generalized Inverse Exponential Distribution Based on URRSS

This paper deals with the Bayesian estimation of Shannon entropy for the generalized inverse exponential distribution.Assuming that the observed samples are taken from the upper record ranked set sampling(URRSS)and upper record values(URV)schemes.Formulas of Bayesian estimators are derived depending on a gamma prior distribution considering the squared error,linear exponential and precautionary loss functions,in addition,we obtain Bayesian credible intervals.The random-walk Metropolis-Hastings algorithm is handled to generate Markov chain Monte Carlo samples from the posterior distribution.Then,the behavior of the estimates is examined at various record values.The output of the study shows that the entropy Bayesian estimates under URRSS are more convenient than the other estimates under URV in the majority of the situations.Also,the entropy Bayesian estimates perform well as the number of records increases.The obtained results validate the usefulness and efficiency of the URV method.Real data is analyzed for more clarifying purposes which validate the theoretical results.

About the Mean Difference of the Inverse Normal Distribution

The calculation of the mean difference for the inverse normal distribution can be obtained by a transformation of variable or a hard integration by parts. This paper shows a simpler formula of the mean difference of the inverse normal distribution that highlights the role of the two parameters on the mean difference of the model. It makes it easier to study the relation of the mean difference with the other indexes of variability for the inverse normal distribution.

A New Modified Inverse Lomax Distribution: Properties, Estimation and Applications to Engineering and Medical Data

In this paper,a modified form of the traditional inverse Lomax distribution is proposed and its characteristics are studied.The new distribution which called modified logarithmic transformed inverse Lomax distribution is generated by adding a new shape parameter based on logarithmic transformed method.It contains two shape and one scale parameters and has different shapes of probability density and hazard rate functions.The new shape parameter increases the flexibility of the statistical properties of the traditional inverse Lomax distribution including mean,variance,skewness and kurtosis.The moments,entropies,order statistics and other properties are discussed.Six methods of estimation are considered to estimate the distribution parameters.To compare the performance of the different estimators,a simulation study is performed.To show the flexibility and applicability of the proposed distribution two real data sets to engineering and medical fields are analyzed.The simulation results and real data analysis showed that the Anderson-Darling estimates have the smallest mean square errors among all other estimates.Also,the analysis of the real data sets showed that the traditional inverse Lomax distribution and some of its generalizations have shortcomings in modeling engineering and medical data.Our proposed distribution overcomes this shortage and provides a good fit which makes it a suitable choice to model such data sets.

Generalized Marshall Olkin Inverse Lindley Distribution with Applications

In this article,a new generalization of the inverse Lindley distribution is introduced based on Marshall-Olkin family of distributions.We call the new distribution,the generalized Marshall-Olkin inverse Lindley distribution which offers more flexibility for modeling lifetime data.The new distribution includes the inverse Lindley and the Marshall-Olkin inverse Lindley as special distributions.Essential properties of the generalized Marshall-Olkin inverse Lindley distribution are discussed and investigated including,quantile function,ordinary moments,incomplete moments,moments of residual and stochastic ordering.Maximum likelihood method of estimation is considered under complete,Type-I censoring and Type-II censoring.Maximum likelihood estimators as well as approximate confidence intervals of the population parameters are discussed.A comprehensive simulation study is done to assess the performance of estimates based on their biases and mean square errors.The notability of the generalized Marshall-Olkin inverse Lindley model is clarified by means of two real data sets.The results showed the fact that the generalized Marshall-Olkin inverse Lindley model can produce better fits than power Lindley,extended Lindley,alpha power transmuted Lindley,alpha power extended exponential and Lindley distributions.

Statistical Inference of Sine Inverse Rayleigh Distribution

We study in this manuscript a new one-parameter model called sine inverse Rayleigh(SIR)model that is a new extension of the classical inverse Rayleigh model.The sine inverse Rayleigh model is aiming to provide morefit-ting for real data sets of purposes.The proposed extension is moreflexible than the original inverse Rayleigh(IR)model and it hasmany applications in physics and medicine.The sine inverse Rayleigh distribution can havea uni-model and right skewed probability density function(PDF).The hazard rate function(HRF)of sine inverse Rayleigh distribution can be increasing and J-shaped.Sev-eral of thenew model’s fundamental characteristics,namely quantile function,moments,incompletemoments,Lorenz and Bonferroni Curves are studied.Four classical estimation methods forthe population parameters,namely least squares(LS),weighted least squares(WLS),maximum likelihood(ML),and percentile(PC)methods are discussed,and the performanceof the four estimators(namely LS,WLS,ML and PC estimators)are also compared bynumerical implementa-tions.Finally,three sets of real data are utilized to compare the behavior of the four employed methods forfinding an optimal estimation of the new distribution.

Bivariate Beta–Inverse Weibull Distribution:Theory and Applications

Probability distributions have been in use for modeling of random phenomenon in various areas of life.Generalization of probability distributions has been the area of interest of several authors in the recent years.Several situations arise where joint modeling of two random phenomenon is required.In such cases the bivariate distributions are needed.Development of the bivariate distributions necessitates certain conditions,in a field where few work has been performed.This paper deals with a bivariate beta-inverse Weibull distribution.The marginal and conditional distributions from the proposed distribution have been obtained.Expansions for the joint and conditional density functions for the proposed distribution have been obtained.The properties,including product,marginal and conditional moments,joint moment generating function and joint hazard rate function of the proposed bivariate distribution have been studied.Numerical study for the dependence function has been implemented to see the effect of various parameters on the dependence of variables.Estimation of the parameters of the proposed bivariate distribution has been done by using the maximum likelihood method of estimation.Simulation and real data application of the distribution are presented.

Inverse Length Biased Maxwell Distribution:Statistical Inference with an Application

In this paper,we suggested and studied the inverse length biased Maxell distribution(ILBMD)as a new continuous distribution of one parameter.The ILBMD is obtained by considering the inverse transformation technique of the Maxwell length biased distribution.Statistical characteristics of the ILBMD such as the moments,moment generating function,mode,quantile function,the coefficient of variation,coefficient of skewness,Moors and Bowley measures of kurtosis and skewness,stochastic ordering,stress-strength reliability,and mean deviations are obtained.In addition,the Bonferroni and Lorenz curves,Gini index,the reliability function,the hazard rate function,the reverse hazard rate function,the odds function,and the distributions of order statistics for the ILBMD,are presented.The ILBMD parameter is estimated using the maximum likelihood method,the method of moments,the maximum product of spacing technique,the ordinary and weight least square procedures,and the Cramer-Von-Mises methods.The Fishers information,as well as the Rényi and q-entropies,are derived.To investigate the usefulness of the proposed lifetime distribution and to illustrate the purpose of the study,a real dataset of the relief times of 20 patients receiving an analgesic is used.

Flexible Reduced Logarithmic-Inverse Lomax Distribution with Application for Bladder Cancer

In this paper, a new method for adding parameters to a well-established distribution to obtain more flexible new families of distributions is applied to the inverse Lomax distribution (IFD). This method is known by the flexible reduced logarithmic-X family of distribution (FRL-X). The proposed distribution can be called a flexible reduced logarithmic-inverse Lomax distribution (FRL-IL). The statistical and reliability properties of the proposed models are studied including moments, order statistics, moment generating function, and quantile function. The estimation of the model parameters by maximum likelihood and the observed information matrix are also discussed. In order to assess the potential of the newly created distribution. The extended model is applied to real data and the results are given and compared to other models.

Distributed inverse synthetic aperture radar imaging of ship target with complex motion

For ship targets with complex motion,it is difficult for the traditional monostatic inverse synthetic aperture radar(ISAR)imaging to improve the cross-range resolution by increasing of accumulation time.In this paper,a distributed ISAR imaging algorithm is proposed to improve the cross-range resolution for the ship target.Multiple stations are used to observe the target in a short time,thereby the effect of incoherence caused by the complex motion of the ship can be reduced.The signal model of ship target with three-dimensional(3-D)rotation is constructed firstly.Then detailed analysis about the improvement of crossrange resolution is presented.Afterward,we propose the methods of parameters estimation to solve the problem of the overlap or gap,which will cause a loss of resolution and is necessary for subsequent processing.Besides,the compressed sensing(CS)method is applied to reconstruct the echoes with gaps.Finally,numerical simulations are presented to verify the effectiveness and the robustness of the proposed algorithm.

The Marshall-Olkin Right Truncated Fréchet-Inverted Weibull Distribution: Its Properties and Applications

In this paper, a new probability distribution is proposed by using Marshall and Olkin transformation. Some of its properties such as moments, moment generating function, order statistics and reliability functions are derived. The method of maximum likelihood is used to estimate the model parameters. The graphs of the reliability function and hazard rate function are plotted by taken some values of the parameters. Three real life applications are introduced to compare the behaviour of the new distribution with other distributions.

Modeling Reliability Engineering Data Using Scale-Invariant Quasi-Inverse Lindley Model

An important property that any lifetime model should satisfy is scale invariance.In this paper,a new scale-invariant quasi-inverse Lindley(QIL)model is presented and studied.Its basic properties,including moments,quantiles,skewness,kurtosis,and Lorenz curve,have been investigated.In addition,the well-known dynamic reliability measures,such as failure rate(FR),reversed failure rate(RFR),mean residual life(MRL),mean inactivity time(MIT),quantile residual life(QRL),and quantile inactivity time(QIT)are discussed.The FR function considers the decreasing or upside-down bathtub-shaped,and the MRL and median residual lifetime may have a bathtub-shaped form.The parameters of the model are estimated by applying the maximum likelihood method and the expectation-maximization(EM)algorithm.The EM algorithm is an iterative method suitable for models with a latent variable,for example,when we have mixture or competing risk models.A simulation study is then conducted to examine the consistency and efficiency of the estimators and compare them.The simulation study shows that the EM approach provides a better estimation of the parameters.Finally,the proposed model is fitted to a reliability engineering data set along with some alternatives.The Akaike information criterion(AIC),Kolmogorov-Smirnov(K-S),Cramer-von Mises(CVM),and Anderson Darling(AD)statistics are used to compare the considered models.

Monotonicity of the tail dependence for multivariate t-copula

This paper considers the upper orthant and extremal tail dependence indices for multivariate t-copula. Where, the multivariate t-copula is defined under a correlation structure. The explicit representations of the tail dependence parameters are deduced since the copula of continuous variables is invariant under strictly increasing transformation about the random variables, which are more simple than those obtained in previous research. Then, the local monotonicity of these indices about the correlation coefficient is discussed, and it is concluded that the upper extremal dependence index increases with the correlation coefficient, but the monotonicity of the upper orthant tail dependence index is complex. Some simulations are performed by the Monte Carlo method to verify the obtained results, which are found to be satisfactory. Meanwhile, it is concluded that the obtained conclusions can be extended to any distribution family in which the generating random variable has a regularly varying distribution.

A NEW QUANTITATIVE WAY FOR DETERMINING LEAF AREA INDEX AND NET PRIMARY PRODUCTIVITY IN REGIONAL SCALE

An inversion of bidirectional reflection distribution fiJnedon (BRDF) wastested using NK Model and NOAA AVHRR datu. The test involVed sensitiveanalysis, optimum inversion selecting, ground simulated expenment, calibrahngmeasuremed with satellite and computer image processmg. Results of comparisonwith NDVI indicatal that inversion of BRDF will have brigh developing prospect inthe next decade.

Retrieval of aerosol size distribution using improved quantum-behaved particle swarm optimization on spectral extinction measurements

An improved quantum-behaved particle swarm optimization （IQPSO） algorithm is employed to deter- mine aerosol size distribution （ASD）. The direct problem is solved using the anomalous diffraction approximation and Lambert-Beer＇s Law. Compared with the standard particle swarm optimization algo- rithm, the stochastic particle size optimization algorithm and the original QPSO, our IQPSO has faster convergence speed and higher accuracy within a smaller number of generations. Optimization param- eters for the IQPSO were also evaluated; we recommend using four measurement wavelengths and S0 particles. Size distributions of various aerosol types were estimated using the IQPSO under dependent and independent models. Finally, experimental ASDs at different locations in Harbin were recovered using the IQPSO. All our results confirm that the IQpSO algorithm is an effective and reliable technique for estimatinz ASD.