3: e estimated SF and PP plot of the TIHLIW model. A new six-parameter distribution called the beta generalized inverse Weibull-geometric distribution is proposed. For k = 1, the density function tends to 1/λ as x approaches zero from above and is strictly decreasing. the IW model, see, for example, beta IW by Khan [5], generalized IW by de Gusmão et al. The CDF of the three-parameter TIHLIW distribution follows, by replacing equation (1) in (3), as Keller et al. probability weighted moments and characterizations are obtained. We provide a comprehensive description of the structural properties of the subject distribution and explore some of its special cases. e data refer to relief times of a sample, of 20 patients who receive an analgesic [23]. 3.1. A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced [31], exponentiated transmuted, generalized Rayleigh (ETGR) by Aﬁfy et al. 1: Plots of the PDF and HRF of the TIHLIW distribution for diﬀerent values of parameters. distribution, called odds generalized exponential-inverse Weibull distribution (OGE-IW) is suggested for The importance and flexibility of the proposed family are illustrated by applications to two real data sets. The aim of this paper is to introduce an extension of the inverse Weibull distribution which offers a more flexible distribution for modeling lifetime data. has CDF of TIHLIW distribution, the quantile function (QF), e above equation can be used to generate TIHLIW, random variates. The new model can be more flexible. Browse other questions tagged cdf weibull inverse-cdf or ask your own question. A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced and studied. Production and hosting by Elsevier B.V. Journal of the Egyptian Mathematical Society, https://doi.org/10.1016/j.joems.2017.02.006. A real data application is presented to illustrate the importance of residual life (MRL) has useful applications in economics, life, insurance, biomedical sciences, demography, product, quality control, and product technology (see [19]). e mathematical properties of the TIHLIW, distribution are derived in Section 3. Introduction e importance of. (1)F(x)=e−αx−β,x≥0,α>0,β>0(2)f(x)=αβx−(β+1)e−αx−β,x≥0,α>0,β>0. The inverse Weibull distribution with parameters shape = a and scale = shas density: f(x) = a (s/x)^a exp(-(s/x)^a)/x for x > 0, a > 0 and s > 0. The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. TIHLIW parameters are estimated via four methods, namely, the maximum likelihood, least squares, weighted. e density function of the TIHLIW can be expressed as a linear combination of the inverse Weibull, densities. We introduce a new family of continuous distributions called the odd Lomax-G class and provide four special models. the ordinary and incomplete moments, generating function, Renyi and Shannon entropies, order statistics, The importance of the TIHLIW model is studied via a real data application. Plots of the PDF and HRF of the TIHLIW distribution for different values of parameters. Further, the IW model has many, important applications in reliability engineering, infant, mortality, useful life, wear-out periods, life testing, and, e cumulative distribution function (CDF) of the IW, Its associated probability density function (PDF) has the, e statistical literature contains several extensions of. The inverse Weibull (IW) distribution is also known as reciprocal Weibull distribution (see [1, 2]). 2. In this paper, we propose a new lifetime model called the type I half-logistic inverse Weibull (TIHLIW) model. Developing probability distributions their application and statistical inferences for modelling data coming from diverse area. close ﬁts to relief times data than other ﬁtted models. modeling lifetime data. Some statistical properties of the MOEIW are explored, such as quantiles, moments and reliability. We introduce a new family of continuous distributions called the beta transmuted-H family which extends the transmuted family pioneered by Shaw and Buckley (2007). [2] and are based on the Kumaraswamy distribution. In addition, comparisons to other models are carried out to illustrate the flexibility of the proposed model. to estimate the [15] proposed the extended odd, Weibull-G, and Cordeiro et al. [7], Kumaraswamy generalized IW by Oluyede and Yang [8], Kumaraswamy modified IW by Aryal and Elbatal [9], Marshall-Olkin IW by Okasha et al. The maximum likelihood method is used 2: e mean values and MSEs of the TIHLIW distribution. Kumaraswamy modiﬁed IW by Aryal and Elbatal [9], Marshall-Olkin IW by Okasha et al. A new A new six-parameter distribution called the beta generalized inverse Weibull-geometric distribution is proposed. Its characterization and statistical properties are obtained, such as reliability, moments, entropy and order statistics. The generalization are motivated by the recent work of Cordeiro et al. These estimators are compared via some simulations in Section 5. The maximum likelihood method is used for estimating the model parameters, and the finite sample performance of the estimators is assessed by simulation. generate more ﬂexible extended distributions. Kumaraswamy generalized IW by Oluyede and Yang [8]. Journal of Nonlinear Science and Applications, Pakistan Journal of Statistics and Operation Research. The kth raw moment of the random variable X isE[X^k], k < shape, and the kthlimited moment at some limit d is E[min(X, d)^k], all k. The statistical literature contains several extensions of the IW model, see, for example, beta IW by Khan [5], generalized IW by de Gusmão et al. and weighted least square methods are used to estimate the, parameters of beta distribution [20]. The corresponding PDF of (4) reduces to For example, Marshall and Olkin [12] proposed Marshall-Olkin-G, Shaw and Buckley [13] defined transmuted-G, Cordeiro and de Castro [14] pioneered Kumaraswamy-G, Alizadeh et al. The proposed model can be used, as a good alternative to some existing distributions, in modeling several real data. The new distribution is generated from the logit of a beta random variable and includes the generalized inverse Weibull geometric distribution.Various structural properties of the new distribution including explicit expressions for the moments, moment generating function, mean deviation are derived. The inverse Weibull (IW) distribution has been used to model, many real life applications for example degradation of mechanical components such as pistons, crankshafts of diesel engines, as well as breakdown of insulating fluid. Further, the IW model has many important applications in reliability engineering, infant mortality, useful life, wear-out periods, life testing, and service records (see [4]). [17] proposed the type I half-logistic-G, (TIHL-G) class. Let, from the TIHLIW distribution, and then the LSEs and, Further, the LSEs and WLSEs of the TIHLIW parameters, are also obtained by solving the following nonlinear equa-, (CVM) method [21, 22], the CVMEs of the TIHLIW pa-, rameters can be constructed by minimizing, obtained by solving the following nonlinear equations si-, In this section, we conduct a simulation study to compare, the performance of the diﬀerent estimators based on the, mean square error criterion. 4: Goodness-of-ﬁt measures for relief times data. Interested in research on Weibull Distribution? A simulation study is performed to evaluate the precision of the estimates from both methods.