We propose a new wider family called the weighted Lindley-G family. We derive some mathematical properties and special sub-models of the new family. We address the estimation of the model parameters by eight approaches of estimation. The estimation approaches are ranked and compared by using detailed simulations to develop a guideline for choosing the best approach for estimating the distribution parameters. The potentiality of the new family is illustrated via two applications to real-life data. It is shown that the proposed WLi-G family is more flexible as compared to some of the most cited families in the distribution theory literature such as the exponentiated-G, beta-G, transmuted-G, and alpha-power-G families under the same baseline model.
AfifyA.Z., GemeayA.M. and IbrahimN.A., The heavy-tailedexponential distribution: risk measures, estimation, and applicationto actuarial data, Mathematics8 (2020), 1276.
2.
AfifyA.Z., YousofH.M., AlizadehM., GhoshI., RayS. and OzelTheG., Marshall-Olkin transmuted-G family of distributions, Stochastics and Quality Control35 (2020), 79–96.
3.
AljohaniH.M., BandarS.A., Al-MoflehH., AhmadZ., El-MorshedyandM. and AfifyA.Z., A new asymmetric extended family: properties andestimation methods with actuarial applications,e, Plos One17 (2022), 0275001.
4.
AlmazahM.M.A., AlnssyanB., AhmedA.H.N. and AfifyReliabilityA.Z., properties of the NDL family of discrete distributionswith its inference, Mathematics9 (2021), 1139.
5.
AlzaatrehA., LeeC. and FamoyeF., A new method for generatingfamilies of continuous distributions, Metron71 (2013), 63–79.
6.
AndersonT.W. and DarlingD.A., Asymptotic theory of certain”goodness of fit” criteria based on stochastic processes, TheAnnals of Mathematical Statistics32 (1952), 193–212.
7.
ChengR., AminN. Maximum Product of Spacings Estimation with Application to the Lognormal Distribution, (Mathematical Report 79-1; University of Wales IST: Cardiff, UK, 1979.
8.
ChengR. and AminN., Estimating parameters in continuous univariatedistributions with a shifted origin, J.R. Stat. Soc. Ser.B-Stat. Methodological45 (1983), 394–403.
9.
ChoiK. and BulgrenW.G., An estimation procedure for mixtures ofdistributions, Journal of the Royal Statistical Society: SeriesB (Methodological)30 (1968), 444–460.
10.
CordeiroG.M., AfifyA.Z., YousofH.M., PescimR.R. and AryalTheG.R., exponentiated Weibull-H family of distributions: Theory andApplications, Mediterranean Journal of Mathematics14 (2017), 1–22.
11.
CordeiroG.M., AlizadehM. and DinizP.R., Marinho, The type Ihalf-logistic family of distributions, Journal of StatisticalComputation and Simulation86 (2016), 707–728.
12.
CordeiroG.M. and deM., Castro, A new family of generalizeddistributions, Journal of Statistical Computation andSimulation81 (2011), 883–898.
13.
EugeneN., LeeC. and FamoyeF., Beta-normal distribution and itsapplications, Commun. Stat. Theory Methods31 (2002), 497–512.
14.
GuptaR.C., GuptaP.L. and GuptaR.D., Modeling failure time data byLehman alternatives, Commun. Stat. Theory Methods27 (1998), 887–904.
15.
GuptaR.D. and KunduD., Exponentiated exponential family: analternative to gamma and Weibull distributions, BiometricalJournal: Journal of Mathematical Methods in Biosciences43 (2001), 117–130.
16.
JonesM.C., Families of distributions arising from distributions oforder statistics, Test13 (2004), 1–43.
17.
KhanM.S., KingR. and HudsonI., Transmuted generalized exponentialdistribution: a generalization of the exponential distribution withapplications to survival data, Commun. Stat. Simul.Comput.46 (2017), 4377–4398.
18.
LanY. and LeemisL.M., The logistc-exponential survivaldistribution, Naval Research Logistics55 (2008), 252–64.
19.
MahdaviA. and KunduD., A new method for generating distributionswith an application to exponential distribution, Commun. Stat.Theory Methods46 (2017), 6543–6557.
20.
MarshallA.W. and OlkinI., A new method for adding a parameter to afamily of distributions with application to the exponential andWeibull families, Biometrika84 (1997), 641–652.
21.
MeadM.E., AfifyA.Z. and ButtN.S., The modified KumaraswamyWeibull distribution: properties and applications in reliability andengineering sciences, Pakistan Journal of Statistics andOperation Research16 (2020), 433–446.
22.
MurthyD.N.P., XieM., JiangR. Weibull Models, John Wiley & Sons Inc., Hoboken, NJ, 2004.
23.
NofalZ.M., AltunE., AfifyA.Z. and AhsanullahM., The generalizedKumaraswamy-G family of distributions, Journal of StatisticalTheory and Applications18 (2019), 329–342.
24.
ShamaM.S., El KtaibiF., Al AbbasiJ.N., ChesneauC. and AfifyA.Z., Complete study of an original power-exponentialtransformation approach for generalizing probability distributions, Axioms12 (2023), 67.
25.
ShawW.T., BuckleyI.R. The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map, UCL discovery repository, https://doi.org/10.48550/arXiv.0901.0434.
26.
SwainJ., VenkatramanS. and WilsonJ., Least squares estimation ofdistribution function in Johnsons translation system, J. Stat.Comput. Simul.29 (1988), 271–297.
27.
TahirM.H. and NadarajahS., Parameter induction in continuousunivariate distributions: well-established G families, Anais daAcademia Brasileira de Ciéncias87 (2015), 539–568.
