MOMENT GENERATING FUNCTIONS OF RANDOM VARIABLES AND ASYMPTOTIC BEHAVIOUR FOR GENERALIZED FELLER OPERATORS

Describes the representation of moment generating function for the S-lambda type random variables. Higher order asymptotic formula for generalized Feller operators; Regular n-r order moment for the random variables.

The New Mixed Generalized Erlang Distribution

In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by wi ≥ 0 and . These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by wi ∈ R, and maintaining . Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments.

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.

A Linear Immigration-Birth-Death Model and Its Statistical Inference

In this paper, we employ moment generating function to obtain some exact formula of transition probability of immigration-birth-death(IBD) model and discuss the simulation of sample path and statistical inference with complete observations of the IBD process by the exact transition density formula.

Likelihood Inference under Generalized Hybrid Censoring Scheme with Comp eting Risks

Statistical inference is developed for the analysis of generalized type-Ⅱ hybrid censoring data under exponential competing risks model. In order to solve the problem that approximate methods make unsatisfactory performances in the case of small sample size,we establish the exact conditional distributions of estimators for parameters by conditional moment generating function(CMGF). Furthermore, confidence intervals(CIs) are constructed by exact distributions, approximate distributions as well as bootstrap method respectively,and their performances are evaluated by Monte Carlo simulations. And finally, a real data set is analyzed to illustrate all the methods developed here.

Analysis of asymptotically tight approximation SER for cooperative NOMA systems

The closed-form formula derivation of the power domain cooperative non-orthogonal multiple access(NOMA)system is of great significance for further improving the performance of the system.However,the system performance formulas of the channel capacity and the paired bit error rate pairwise error probability(PEP)are too complicated,which have increased the difficulty in system performance optimization.Therefore,based on the amplify forward(AF)relay cooperative NOMA model,the signal interference noise ratio(SINR)formulas of the two user nodes are constructed.Through the assumption of that,the symbol error rate(SER)of each user is fair,the simplification condition of moment generating function(MGF)with the harmonic mean form is satisfied.Combined with the SER calculation formula of MGF,the system SER asymptotically tight approximation formula with simple structure is derived at high signal-to-noise ratio(SNR).The Monte Carlo simulation results show that,the formula can accurately describe the SER performance of the power domain cooperative NOMA system with the non-ideal successive interference cancellation(SIC)system when SNR is high.Under the condition of certain total power,the optimal power allocation factor is solved in order to minimize the total system SER.

On the Application of Nadarajah Haghighi Gompertz Distribution as a Life Time Distribution

The convolution of Nadarajah-Haghighi-G family of distributions will result into a more flexible distribution (Nadarajah-Haghighi Gompertz distribution) than each of them individually in terms of the estimate of the characteristics in there parameters. The combination was done using Nadarajah-Haghighi (NH) generator. We investigated in the newly developed distribution some basic properties including moment, moment generating function, survival rate function, hazard rate function asymptotic behaviour and estimation of parameters. The proposed model is much more flexible and has a better representation of data than Gompertz distribution and some other model considered. A real data set was used to illustrate the applicability of the new model.

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.

Inferences in Linear Mixed Models with Skew-normal Random Effects

For the linear mixed model with skew-normal random effects, this paper gives the density function, moment generating function and independence conditions. The noncentral skew chi-square distribution is defined and its density function is shown. The necessary and sufficient conditions under which a quadratic form is distributed as noncentral skew chi-square distribution are obtained. Also, a version of Cochran＇s theorem is given~ which modifies the result of Wang et al. （2009） and is used to set up exact tests for fixed effects and variance components of the proposed model. For illustration, our main results are applied to a real data problem.

Exact Inference for Joint Type-I Hybrid Censoring Model with Exponential Competing Risks Data

Assuming that the failure time under different risk factors follows the independent exponential distribution, a joint model under Type-I hybrid censoring is addressed in detail. Based on the Maximum likelihood estimates （MLEs） of unknown parameters, we obtain exact distributions of MLEs by using the moment generating function （MGF）. Confidence intervals （CIs） of parameters are constructed through both the exact method and the parametric bootstrap method. Then we compare the performances of different methods by Monte Carlo simulations. Finally, the validity of the proposed models and methods are demonstrated by a numerical example.

Statistical Inference for a Simple Step Stress Model with Competing Risks Based on Generalized Type-ⅠHybrid Censoring

This paper investigates a simple step-stress accelerated lifetime test(SSALT)model for the inferential analysis of exponential competing risks data.A generalized type-I hybrid censoring scheme is employed to improve the efficiency and controllability of the test.Firstly,the MLEs for parameters are established based on the cumulative exposure model(CEM).Then the conditional moment generating function(MGF)for unknown parameters is set up using conditional expectation and multiple integral techniques.Thirdly,confidence intervals(CIs)are constructed by the exact MGF-based method,the approximate normality-based method,and the bias-corrected and accelerated(BCa)percentile bootstrap method.Finally,we present simulation studies and an illustrative example to compare the performances of different methods.