Introduction :-

       The Department of Statistics, University of Mumbai was established in the year 1948.  It was the first Department  in the western region, for postgraduate studies and research in Statistics.  The Department has completed 57 years of existence.  It offers postgraduate courses leading to the Master of Arts and Science (M.A./M.Sc.) degree, by papers, awarded by the University of Mumbai.  In addition to the master's programme, M.Phil. and Ph.D. degree programmes are also undertaken by the Department.  Experienced faculty of the Department is devoted to research in their respective areas of specialization.  Research and teaching are given equal importance by the faculty.  Extra care is taken to pay individual attention to the student in their laboratory work and tutorial sessions.  Project work and problem sessions are encouraged to develop innovative and analytical approach to statistics learning.  The Department has a long cherished history of having produced eminent academicians and successful statisticians in the Industry. It is the only center of the University of Mumbai for conducting M.Sc., M.Phil. and Ph.D. programmes.

Location :-

      The Department of Statistics is housed in Lokmanya Tilak Bhavan located in well planned Vidyanagari Campus of the University of Mumbai.  The Vidyanagari Campus is off the C.S.T. Road (now known as Vidyanagari Marg) near Kalina and is accessible from Kurla on Central Railway and Santacruz on Western Railway. BEST bus route 318, 313 and 37 flying between Kurla [West] (CENTRAL Railway) and 318, 313 and 306 Santacruz [East] (WESTERN Railway) pass via vidyanagari.  Also 312 flying between SEEPZ and Prabodhankar Thakre Marg, 374 Ltd. between Goregaon and B.A.R.C. Anushaktinagar pass via vidyanagari.

Accomodation :-

        There are Girls' and Boys' hostels within the Campus. Two rooms in Boys' hostel and two rooms in Girls hostel are reserved for the Department students.

Placement  Committee :-

         The students of M.A./MSc. Statistics (Part I and II) form the placement committee.  The committee mainly consists of the students from the Second year.  They undertake many tasks, the prime one being that of looking after the campus interviews.  They prepare the department brochures and post them to selected companies and those possible to visit, are handed over the brochures by the members.  The companies then visit the campus for recruitment.

        The recruitments are carried for the Part II students.  Each and every student of the Second year has to fill the placement form which is an undertaking stating the rules of the Placement Committee.  The details of the visit of the companies are taken care by the committee.  The committee also organizes other intellectual events.  They conduct meeting on a regular basis to put forth their problems and discuss the agenda.  The committee is thus a representation of the students and act as the layer between the students and the department.

 Companies where our students are placed:

                AC Nielsen-ORG MARG

                American Express

      Aventis Pharma

      Bayer India Ltd.

      Blue Star

      Birla Sunlife

      Business India Group

      Crosstab

      Code Links Data Service

      Citibank

      DIREM

      Dr. Reddy's Lab

      German Remedies

      GE Capital

      Godphrey Philips

      HDFC

      ICICI Prudential

      IMRB

      India Soft Technologies Pvt. Ltd.

      Novartis

      Om Kotak Mahindra Life Insurance

      Pfizer

      Quintiles Spectral

      Research International

      Reserve Bank of India

      Sun Pharma

      Siemens

      SAS Institute

      Telco

      Worldwide Network Services
 

Fees :
          M.Sc. Part ?I
          Academic Year 2005-2006

WORKING PAPERS/RESEARCH PAPERS :

    1.  Professor  Ulhas  J. Dixit

1.                     With Y.S. Sathe), Estimation of P[X ? Y] in negative binomial distribution,  Journal

2.                     of Statistical planning and Inference 83-92, 93, 2001.

3.                     (With Parviz F. Nasiri), Estimation of parameters of the exponential distribution in the presence

4.                     of outliers generated from uniform distribution, METRON, Vol. LIX n. 3-4, 187-198,2001

5.                     (Invited) (With Sarode D.D.) Study of compressive Strength of Concrete of Certain Flyovers

6.                     in Mumbai: The 6^th World Multiconference on Systemic, Cybernetics and Informatics,

7.                     Industrial Systems and Engineering III,Edited by Nagib Callaos,Yigang He and Jorge A.

8.                     Perez-Peraza,Vol,XVII,381-387,2002.

9.                     (With Reddy M.V.): Study  of  Performance of  First Year USP students with respect to their

10.                  Form Seven Marks,  South Pacific Journal of  Natural Sciences,Vol.20,p. 45-47,2002

11.                  (With Dixit, V.U. and Reddy M.V.) Performance of FCAE Diploma holders at USP,

12.                  South Pacific Journal of Natural Sciences, Vol. 20, P. 62-63,2002. 

13.                  (With V.U. Dixit), Testing of the parameters of a right truncated exponential distribution,

14.                  American Journal of  Mathematical and Management sciences,Vol. 22,

15.                  Nos. 3 & 4,343-351,2003

16.                  (With Ali, M. M. and Woo Jungsoo):  Efficient Estimation of parameters of a uniform

17.                  distribution in the presence of outliers, Soochow Journal of Mathematics,

18.                  Vol.29, No.4, P.363-369, 2003 

19.                  (With  K. D. Phal) : Estimation of  a scale parameter of  a truncated gamma distribution,

20.                  Accepted in Soochow  Journal  of  Mathematics  Taipei,Taiwan , 2005

21.                  (With  Muni  Reddy): Mathematics Diagnostic Test for MA111 student at USP-Yes or  No ? ,

22.                  Accepted  in  Journal of  Fijian Studies, 2005 .

    2. Professor  (Mrs)  Smita  P. Nabar

        1. (With S.P.Barpande): A note on maximum likelihood estimator of the mode of
           binormal distribution Bin( s ,?,ks), Journal of Indian Statistical
           Association,Vol.39,No.2, 2001

        2. (with  S.C.Deshmukh) : On estimation of parameters of bolognormal distribution,
              Journal of Indian Statistical Association,Vol.40,No.2, 2002

        3. (With S.P.Barpande): Inference on P( Y < X) in the Binomial distribution,
              Journal of The Indian Association for Productivity,
              Quality and Reliability (IAPQR Transactions),Vol. 28,No.1, 2003,

        4.  (With J.I. Sipahimalani): Performance of a Laboratory in Proficiency Testing
             evaluation by Z-score : 4 easy steps : IDMA Bulletin XXXV(10),2004

    3.  Dr. (Mrs.) Vaijayanti U. Dixit

   1. (Invited) Left handed persons and related issues: The 6^th World Multiconference
 on Systemics,Cybernetics and Informatics Proceedings,Vol. XIII, 2002

        593-597, edited by Nagib Callaos,Greg Whymark and William Lesso 

    2.  (with U.J. Dixit) Testing of Parameters of a Right Truncated Exponential Distribution,

       American Journal of Mathematics and Management sciences,Vol. 29,No. 4 , P.

        363-369, 2003.

    3.  Estimation of parameters of mixed failure time distribution based on a extended modified

        sampling scheme; Commun. In Statist. Theory and Methods,  2003, Vol. 32(10),

        1911-1923.

    4.   (with  U.J. Dixit  and M.V. Reddy)  :  Performance  of  FCAE  Diploma holders at USP;

   South Pacific Journal of Natural Sciences;2002, Vol. 20, pp. 62-63

Research Summary :  

          The maximum likelihood are uniformly minimum variance unbiased estimated (UMUVUE) of P [X≤Y] are derived, when both X & Y have negative binomial distribution whose exact variance is calculated in both the methods.  It has been shown that UMVUE is better than the m/e in case of geometric distribution.  This work is published in JSPI(2001).

            Consider spread from a print source, for example, which might be a small plot
of plants.  During favourable weather conditions, the plants release their pollen &
it disperses according to an exponential distribution with distance from the source.
However, in less favourable conditions light, rain or mist, not only are the plants less
likely to release pollen, but that which is released still falls with an exponential
distribution with a different scale parameter.  Dixit, Moore and Barnett (1996) consider
the above example in the context of spread disease amongst plants of viral spores such
as barley yellow mosaic dwarf virus (BYMDV).  By using the methodology as stated in
 Dixit, Moore & Barnett (1996), it is possible to estimate the average distiance (and
 hence area) of disease spread in a field from a small patch of infested plants in
the presence of some spread caused by insects.

            According to Dixit, Moore and Barnett (1996), we assume that a set of random variables (X1, X2, ?.., Xn) represent the distance of an infected sampled plant from a plot of plants inoculated with a virus.  Some of the observations are derived from the airborne dispedrsal of the spores and are distributed according to the exponential distribution.  The other observations out of n random variables (s by K) are present because abhids which are known to be carriers of BYMDV have passed the virus into the plants when the aphids feed on the sap. This K aphids one considered to be uniformly distributed.  In this case Dixit and Nasiri (2001) had derived the maximum likelihood, moment and mixture estimators for sample from the exponential distribution in the presence of outliers generated from uniform distribution.  Hence it is shown that mixture, estimators are better than maximum likelihood and moment estimators.

            ?A statistical analysis is carried out using their Cumulative Grade Point Average (CGPA) to see if there is a significant difference between the performance of the first year (100 level) student at the University of the South Pacific (USP) having different form- 7 marks.  For this analysis relevant data was obtained for the years 1997- 2001 and the Form Seven marks (Total of English and best 3 subjects)  were divided into the classes 250-259, 260- 269, and ≥ 270.  Results indicate that there is a significant difference between the CGPA of these three classes.  A further analysis is then carried out by using the CGPA of only the first two classes 250 ?259 and 260- 269 in order to determine if an increase in the entry requirements from 250 to 260 will be justified.  Under its current admission regulations, USP accepts into its degree programmes all students who have passed the seventh form examination with an aggregate of at least 250 marks out of 400 with a minimum of 50% in English.  The results of our analysis indicate that the minimum entry requirement could be increased to 260 if USP feels that the level of significance (Type I Error) is more than 3.17 percent.  However, the minimum entry level should remain as 250 if the significance level is at most 3.17 percent.  See Dixit and Reddy (2002):

 The University of the South pacific (USP) is currently attracting many students who have completed a Diploma at the Fiji College of Advanced Education (FCAE) into its study programmes.  These students are not required to do certain courses, mostly those at the first year level, as they had done courses of a similar nature at FCAE and hence these are cross-credits for these FCAE courses is program at USP.  In order to ensure that the granting of cross-credits for these FCAE courses is justified, USP needs to study the performance of these students.  In this paper, we have carried out a statistical analysis using the Cumulative Grade Point Averages (CGPA) of all 67 such students.  Results of the analysis indicate that the performance of these students justifies the granting of cross-credits.

          Dixit & Dixit (2003) had obtained optimum test of hypothesis about the parameter c (truncation point) and θ(scale parameter) of a right truncated exponential distribution.

          Dixit and Sarode (2002) had done the work on ?study of compressive strength of concrete of certain flyovers in Mumbai.

          Dixit, Ali and Woo.J. (2003) had given efficient estimators of parameters of a uniform distribution in the presence of outliers.  Currently, Dixit and Phal (2005) had considered the estimation of a scale parameter of a truncated gamma distribution.

          Skewness can be introuduced into general Symmetric distributions.  For example two-piece normal distribution or Binormal distribution as studied in Kimber (1985).  Nabar & Barpande (2002) had studied the model Binormal (σ, μ, kσ) and shown that there exists a unique solution of the likelihood equation for estimating μ. And estimation of P(Y<X) for this model was studied in Nabar & Barpande (2003).  On the same lines two piece Bilognormal distribution was introduced by Nabar and Deshmukh (2002) and two piece logistic distribution by Nabar and Deshmukh (2004).  We call these distributions as change point distributions.  They have applications in climatological studies, finance, ionimplantation etc.

         At present we have obtained the ephsilon skew representation of these distributions and also two-piece Laplace distribution.

        The problem of estimation & testing of parameters of a mixture of  degenerate  (degenerate at Zero) and exponential distribution is considered.  A modified sampling scheme is proposed and the finite sample and asymptotic properties of the estimators are studied; see Dixit (2003)

         Left-handed persons and related issues are studied.  The proportion of left-handed persons is estimated (after defining left handedness). Association of left-handedness with sex, occupation, educational background and job satisfaction is checked using some statistical tests, see Dixit (2002).

 Annual Report :

 1.  Professor Y.S. Sathe  had delivered a series of lectures on ?Financial mathematics? in 
      the year 2004-2005.

2.  Professor Dixit U.J. , Professor Shenoy R.G. & Dr. Dixit V.U. delivered a series of lecture on ?Applications of statistical Techniques? & specially on logistic regression at Fractal Analytics Ltd..

3.   Professor (Mrs.) Nabar S.P. had delivered a lecture in ?mathematical Reasoning? at ?Administrative training cell? in the University.

4.   All faculty members delivered a series of lectures for refresher course, conducted by the Department of mathematics in the month of March 2005.

5.   Professor Shenoy R.G. delivered a series of lectures on ?stochastics process? at SNDT University.

6.   Professor Dixit U.J. delivered a lecture in ?Data Analysis? at Ruia college.

7.  Professor Shenoy R.G.  inaugurated statistical club of B.N. Bandodkar College .  Our department had conducted a seminar on ?applications of Statistics? Following speakers were invited:

          1.     Prof. Govind Mudholkar

2.     Shri A.S. Arekar

3.     Shri S.K. Kumra

4.     Dr. Chitra Lele

5.     Dr. Oak Prashant

6.     Shri. R.K. Reddy

7.     Shri Shailesh Gadre

8.   Professor (Mrs.) Nabar worked on ?Glycon registry Project for Aventics Pharma.