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New Generalizations of Power Cauchy Distribution

Thesis Info

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Author

Zubair, Muhammad

Program

PhD

Institute

The Islamia University of Bahawalpur

City

Bahawalpur

Province

Punjab

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Statistics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/11329/1/th-zubair_19_july_19_Revision-2.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726751939

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Four new generalizations of power-Cauchy distribution are proposed in this thesis. Firstly, the Poisson-X family is proposed and its important mathematical properties are obtained. Then, a member of the Poisson-X family namely the Poisson power-Cauchy)distributionisdefinedanditsstructuralpropertiesareinvestigated. The proposed model is fitted to three real-life data sets to illustrate its flexibility. Secondly, the log-odd normal generalized family of distributions is introduced. Then, a special model of this family, the log-odd normal power-Cauchy is defined and its mathematical properties are obtained. A real-life data set is used to prove the superiority of the proposed model. Thirdly, the Weibull-Power-Cauchy distribution is proposed and its mathematical properties are obtained. Two useful characterizations based on truncated moments are also presented. The proposed model is applied to three real-life data sets to investigate its flexibility. Lastly, a new extensionofpower-Cauchymodelisproposedbycompoundingthepower-Cauchyand negative-binomial distribution called the power-Cauchy negative-binomial distribution. Some mathematical properties of the proposed model are obtained and the model parameters are estimated using the maximum likelihood method. A simulation study is carried out to investigate the performance of maximum likelihood method. The flexibility of the proposed model is illustrated through three real-life data sets. Then, a new class of regression model is introduced for location and scale based on the logarithm of the proposed random variable and, estimation and inference on the regression coefficients are discussed.
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وفات

۲۰ مئی ۱۹۷۹ء کوعلاج کےلئے امریکہ گئے اور۲۲ ستمبر ۱۹۷۹ء کو بفیلو ہسپتال میں آپ کاانتقال ہوا ۔

فقہ اسلامی میں قسامت کا تصور

Islam lays great emphasis on security and the sanctity of human life. The holy Quran terms killing of an innocent person as killing of the whole humanity. It prohibits unjust killing of human being in unequivocal terms. The holy Qur’an and Sunnah terms killing of an innocent person as one of the greatest sins. An eternal torment is the destiny of a killer who takes life of a person unjustly. However, it is also a bitter fact that hardly   a crime free society could be found   anywhere in the world. Peace prevails only in those societies where culprits are brought to justice. This is why Islamic penal code has prescribed punishments for all kinds of crimes. It has prescribed punishment of Qisâs in case of intentional murder and Diyat (blood money in case of killing of a person by mistake, it is also due in case if remission is made by the heirs in intentional murder case). To prove the crime of murder, testimony of two reliable witnesses or confession of the killer is required before the court. However, if a corpse is found in a place where killer is unknown and witnesses are unavailable,    then Islam enjoins the process of Qasâmah to safeguard rights of the heirs of the deceased. Qasâmah is a process of taking oath by fifty persons selected by the heirs of the slain. In this article the concept of Qasâmah has been elaborated. It  has three parts , in the  first part conditions for the validity of  Qasâmah has been elaborated, while in the second part its process has been discussed with elaborate opinions  of jurists  regarding taking of  oath, as some of them opine that  the  heirs of the slain  have to take oath, mentioning name of the killer,   while others say  oath will be taken by the defendants that they  didn’t kill him, Both these opinions  have been discussed by producing arguments of  the both sides. While in the third part the issue of Qisâs and Diyat has been discussed as according to some jurists the Qasâmah entails Qisâs while other say that it entails Diyat only; arguments of both sides have been discussed in detail.

Taxonomic Studies of Fossil Even and Odd- Toed Mammals from the Miocene Rocks of Dhok Bun Ameer Khatoon, District Chakwal, Punjab, Pakistan

Fossil site Dhok Bun Ameer Khatoon (32o 47'' 26.4" N, 72° 55'' 35.7" E) yielded a significant amount of mammalian assemblage including four families of even-toed fossil mammal (Suidae, Tragulidae, Giraffidae, and Bovidae) and one family of odd-toed (Rhinocerotidae) of the Late Miocene. This newly discovered site has well exposed Chinji and Nagri formation and has dated approximately 14.2 Ma-9.5 Ma. This age agrees with the divergence of different mammalian genera and is important Palaeoecologically, Palaeogeographically and Palaeoclimatologically. Sedimentological evidence of the site supports that this is deposited in locustrine or fluvial environment, as Chinji formation is composed primarily of mud-stone while the Nagri formation is sand dominated. Palaeoenvironmental data indicates that Miocene climate of Pakistan was probably be monsoonal as there is now a days. Mostly the genera recovered from this site resemble with the overlying younger Dhok Pathan formation of the Siwaliks while the size variation in dentition is taxonomically important for vertebrate evolutionary point of view and this is the main reason to conduct this study at this specific site to add additional information in the field of Palaeontology. A detailed study of fossils even and odd-toed mammals found in Miocene rocks exposed at Dhok Bun Ameer Khatoon was carried out. Over all one hundred and twenty specimens were collected during field trips from which forty two specimens are well preserved and identified and are described in this thesis. Two specimens belonging to Gaindatherium browni, five specimens belonging to Listriodon pentapotamiae, four specimens belonging to Dorcatherium majus, one specimen belonging to Dorcatherium cf minus, two specimens belonging to Giraffa priscilla, twenty one specimens belonging to Giraffokeryx punjabiensis, three specimens belonging to Gazella sp. and three specimens belonging to Eotragus sp. Dhok Bun Ameer Khatoon is the new locality which is discovered in detail first time in Pakistan by the present author. The collection comprises isolated upper and lower teeth and fragments of maxillae and mandibular ramii.