Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name



Research and Training School (RTS)


Rao, C. Radhakrishna (RTS-Kolkata; ISI)

Abstract (Summary of the Work)

In many diverae scientifie fields, one cones serose experimente where the basie variable unter obaervation ia a direction. We ahall be conoerned, throughout this theais, only with diraations in two-dimensions and wo refer to such a collection of directione an 'circular data or dimenstionl data. In order to make a statintical analyaie of circular data, the first prerequisite is to put thom in a quantitative form. One way of doing thie is to represent the directiona anglea no aaured d thre apeet to eone mui tably choscn sero direation. Al ternately, einee a direetion han no nagni- tude, it can be representod an a unit veetor i.c, as a point an the oirounferenoe of a unit oircle in two dinenatone. Noi ther of thn ge repronentationa for a direetton is uniquo or abeolute aince tho angular value seciened to a direetion would depend on the choior of the zoro dirootion as much an the componenta of the unit veetor depend on tho coordinate eyaton ohonen for represonting the direction. Therefore, it is important to soe that the coneluatona arrived at on analystng the otroul ar population, are indopendent of thone arkitrary valuen anoigned to the dirostions.Exarplca of si tuationa giving niae to circul ar data ea bo found in varioua seicntifie flel da, Por example, geologiati asady tho ortontationn of erona-beddinga and particle long- axon to interpret the diraetion of depositing eurrenta of winda or water. Btudien of the diroctiona of rezanent magne- tien are nonotiaos odo to interpret pal aoonagnetion and ponedble sagnotie pole migrations during goologienl tias. Sistlarly biologisto vorking on bird-atgrationa pertorn oxperizenta an adng-inpigoona which involve abacrving tho direction of night of the hirda a they go out of atght after relonse. beri dea auch eason whore dirocetiona are obacrved an a direct result of the experiaent, abaarvationa on say readen plencuenon oeeuring orer tine or apaou with a regular period of kmom longth L, can be conoeived as obaer- vationn on a olvale with eirounferenoe of length L. Thua the staty of any periodio phonononon, with a portod of knove long ti, given Fiao to an onacntially ninilar problon. Por Oxaplo, ir woe ee atudying a phonononon mupponnd to ihare y diarnal varintton, wi cn trent the 24 Hours of a day an naking up a nyola ad tiras obsain a distri bution of the cecurreneca on the eircunference of a etrele, pooling up the obaervatione ovor nevorel such partada if necessary. Stadies of say the plane-crashea around the yosr or the biologiesl rhythma of living organiana, fall in thts onfegery and ean bo troated as atudios involving diroetional or eircular data.The analyair of eircular data eives rine to a host of novel atatieti dal problene and docs not fit into the fanillar patterna of atasiotionl analyete on the line. Buppo ne the directione have boen given in berna of snglea, then their ari thnetie nosn would not, in goneral, give un a zesningful noan Ä‘ircotion of the sample, nor would the ueual 'standara Ä‘ovistion' give a good mosaure of diaperaton, in general (e.f. Batachelet, 1965). The rcason for this is simple. If the zero dircetion is shifted through a fixed angio, the values of the ri thnetie ean and the atandard deviation calculated on the basis of the new valuce of the obrervations, bear no reasonable algetraie relation to the ariginal valuca sinoe the directione nro menered as anglos nodulo 2R.


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